Low flow fluid controller apparatus and system

ABSTRACT

An air distribution apparatus that serves as a single sensing device for both lighting, LiFi, and HVAC functions that are operable on a single platform by building automation systems. The building automation system may be controllable by a single software system or network accessible locally on site or remotely off site. The air distribution apparatus can operate in a single zone or coupled with multiple like apparatuses for multi-zone operation. It is a high turndown, self-balancing system which allows for continuous commissioning with built-in fault diagnostic systems and that may be used as a supply, return, or exhaust system, or a combination thereof. The air distribution apparatus includes multi-stage airflow control systems that operate progressively based on unique actuation mechanisms and/or algorithms that allow for precise flow control and feedback to self-balance and commission the system.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Division of U.S. application Ser. No. 15/338,166,filed Oct. 28, 2016, entitled “LOW FLOW FLUID CONTROLLER APPARATUS ANDSYSTEM,” which is a Continuation-in-Part of U.S. application Ser. No.15/225,482, filed Aug. 1, 2016, entitled “SELF-BALANCING AIR FIXTURE,”which is a Continuation-in-Part of U.S. application Ser. No. 15/146,447,filed May 4, 2016 entitled “FLUID CONTROL MEASURING AND CONTROLLINGDEVICE,” which is a Continuation-in-Part of U.S. application Ser. No.14/330,941 filed Jul. 14, 2014 entitled “FLUID CONTROL MEASURINGDEVICE,” which claims priority to U.S. Provisional Patent ApplicationNo. 61/872,576 filed Aug. 30, 2013 and entitled “LOW FLOW FLUIDCONTROLLER,” and claims priority to U.S. Provisional Patent ApplicationNo. 61/845,665 filed Jul. 12, 2013 entitled “LOW FLOW DAMPER.” Theentire contents of each of these disclosures are hereby incorporated byreference for all purposes, as if fully set forth herein.

BACKGROUND OF THE INVENTION

Measuring and regulating fluid flows, such as air or water flow, iscommon but typically expensive, particularly for low fluid flows. Inmany cases, costs for measuring low fluid flows may be prohibitive andnot commercially viable. Further, current flow measurement devicesprovide limited turndown ratio, typically less than 10:1, and thereforedo not support accurate measuring functionality for fluid flows. Theselow turn down devices create millions of unnecessary part numbers whichcreates a dysfunctional cumbersome business model. For instance, typicalheating, ventilation, air conditioning (“HVAC”) systems do not performwith accuracy due to the high costs of measuring air flow and limitedturndown. The only option is to run them no lower than it can bemeasured and controlled. This causes the HVAC systems to consumeneedless amounts of energy and also hinders their purpose of providingcomfort to people in a building. Current technology uses large TotalPressure which significantly drains energy. The new technology works onlow Total pressure saving considerable energy.

There is a need for a practical way to measure fluid volumes andregulate the resulting fluid flow. Further, there is a need to do so inan economically viable manner. This disclosure is intended to addressthe above-noted concerns and to provide related advantages.

SUMMARY

This disclosure is generally directed to fluid measurement/fluid controldevices, and more particularly, to a fluid flow measurement, fluidcontrol, analytics and control system. Currently available fluid flowcontrol mechanisms are often based on existing formulas or devices thatcharacterize or measure fluid flow through an orifice. For example,various ducted orifice plate devices have been used to measure fluidflow for well over 100 years.

Advantageously, the instant application discloses new formulas andtechniques which can be implemented for use with fluid control systemsand methods. For example, the instant application describes newcorrelations that resolve contradictions observed between theory andpractice dating back to the 1600's. Specifically, the correlations andrelated techniques disclosed herein, including the Flow and DischargeCoefficient Equations, can be used to address contradictions,inconsistencies, and/or limitations with respect to the vena contractaand other flow phenomena in view of earlier observations, see e.g.Torricelli (1643), Newton (1713), Bernoulli (1738), Borda (1760),Weisbach (1872), Kirchoff (1869), and/or Johansen (1930), as furtherdiscussed elsewhere herein.

A multi-stage damper can be used to address limitations of a standardbutterfly damper, where the butterfly damper can be viewed as a variableorifice plate with projected open area A_(o)=A_(duct)−A_(damper)*

(θ). With a multistage damper such as a two-stage damper, the venacontracta of the inner disk can be controlled, not by the area projectednormal to the duct as in the standard butterfly damper, but by theprojection of the inner annulus opening A₀ normal to the faces of theannulus and opening disk itself.

In one embodiment, a flow device for measuring and controlling a fluidflow through a flow pathway is provided. The flow device may beincorporated in a duct of a heating, ventilation, and air conditioning(HVAC) system. The flow device may comprise an orifice plate positionedwithin the flow pathway and defining a variable opening for receivingflow therethrough. Further, the orifice plate may include an outerassembly comprising a central opening and an inner assembly extendingthrough the central opening. The flow device may further have anactuator assembly operatively connected with the orifice plate.

The inner assembly may comprise a plurality of nested elements, wherebyat least one of the plurality of nested elements includes an additionalopening. In some embodiments, the inner assembly comprises an innerdamper and the outer assembly comprises an outer damper. The outer andinner dampers can me made of various shapes such as square, rectangle,triangle, diamond and more.

In another aspect, the variable opening comprises a plurality ofadditional openings that are arranged in parallel. By way of example, atleast one of the nested elements may be 10 inches in diameter D and anested element 3.5 inches in diameter d, further wherein a scaling ratioD:d of about 10:3.5 is exhibited.

At least one of the inner and outer assemblies may further comprise aplurality of additional assemblies disposed side-by-side in the flowpathway. The inner and outer assemblies may be offset to obtain enhancedflow measurement characteristics. Further, the inner assembly comprisesa non-perforated plate or a perforated plate. In another aspect, atleast one of the inner and outer assemblies may define a shape selectedfrom a group consisting of a circle, triangle, diamond, trapezoid,rectangle, ellipse, sphere, half sphere, and quarter sphere.

A gasket may be disposed on the duct of the flow device and configuredto compress and seal against the outer assembly. The inner and outerassemblies may overlap to define an overlap region, further wherein theoverlap region includes a compressible gasket embedded on at least oneof the inner and outer assemblies. Further, the flow device may includea gasket that provides a tight positive pressure seal between at leasttwo members from the group consisting of an air valve stop, the innerassembly, and the outer assembly. Another design may include the gasketmounted directly on the dampers.

The fluid device may further include a regain section defined by a teardrop nacelle defining at least a portion of the flow pathway downstreamof the orifice plate, wherein the tear drop nacelle reduces losses fromincreased velocity Venturi or Bernoulli effects imparted on the fluidflow upstream of the nacelle. In some embodiments, the flow deviceincludes a hollow outer shaft extending from the outer assembly and aninner shaft extending from the inner assembly through the hollow outershaft, wherein the inner and outer shafts are operatively connected withthe actuator assembly. The actuator assembly may comprise a firstactuator operatively coupled to the hollow outer shaft and a secondactuator operatively coupled to the inner shaft. Furthermore, the firstand second actuators may be collinear and ganged together to enablemeasurability and controllability over a wide flow range. In otherembodiments, the first and second actuators are mounted in parallel oron opposite sides of the flow device.

The actuator assembly may comprise an actuator having a gearing withdual concentric output to rotate the inner and outer assembliesgenerally in sequence or in an overlapping fashion, whereby the gearingcomprises an inner track operatively coupled with the inner shaft and anouter track operatively coupled with the outer shaft. Alternatively, adual race linear or rotational cam may be employed to the same effect.The actuator assembly may include an operating electro-mechanical,pneumatic mechanical device. The actuator may use gears or cables tostroke the shaft mechanism. Further, the actuator assembly may beincorporated with or into a smart device or a device having aprogrammable embedded controller. In a different aspect, the smartdevice includes an algorithm with at least one member selected from agroup consisting of flow measuring, orifice metering and actuatormetering element. The flow device may be a standalone flow measurementdevice.

Furthermore, the orifice plate increases a pressure of the fluid flowfor the purpose of measuring and controlling fluid flow or mass fluidvolume. The orifice plate may split the fluid flow into multiple streamsfor the purposes of increasing velocity pressure or recovering velocitypressure for a more accurate measurement. In some embodiments, the fluidflow measured and controlled by the flow device defines a flow velocitybetween about 5 feet per minute to about 3000 feet per minute inreplacement service, and not over say a recommended 1500 FPM in newdesigns.

In another embodiment, the present disclosure provides a controller inoperative communication with the orifice plate. The controller comprisesa processor and a memory communicatively coupled with and readable bythe processor and having stored therein processor-readable instructionsthat, when executed by the processor, enable the processor to determineflow based on a pressure differential between a first sensor disposedupstream of, and a second sensor disposed downstream of the orificeplate, together with position feedback received from the actuatorassembly, and regulate the variable opening provided by the outer andinner assemblies to effect conformance between measured and desiredflow. The controller may be disposed remotely from the orifice plate andin operative communication with the orifice plate through a networkconnection or a building automation system (BAS).

In other aspects, the first sensor is disposed in the flow pathwayupstream of the orifice plate. The pressure differential may further beobtained relative to a second sensor disposed in the flow pathwaydownstream of the first sensor. The second sensor may be placed behindthe orifice plate in a flow wake or still air in the flow pathway.Further, at least one of the first and second sensors uses or comprisesa shaft that operatively connects the outer or inner assembly with theactuator assembly. For instance, at least one of the first and secondsensors may use the actuator shaft to convey pressure through a ductwall, or may incorporate the sensor opening itself into the shaft. Theshaft may provide at least one of an upstream or a downstream flowmeasuring device or sensor. In some aspects, at least one of the firstand second sensors is a Pitot tube or a multitap linear or crossed Pitottube-like or similar device such as an orifice ring downstream of theorifice plate. In other aspects, at least one of the first and secondsensors comprises a plurality of transducers.

In some embodiments, it is contemplated that the first sensor senses atotal pressure of the fluid flow and the second sensor senses a staticpressure or a diminished representative static pressure of the fluidflow. A difference between first and second sensor pressures yields alarge pressure differential that is capable of measuring smaller fluidvelocities of less than 25 FPM. In some aspects, the first sensor isembedded on an upstream surface of the orifice plate and/or the secondsensor is embedded on a downstream surface of the orifice plate.Furthermore, the orifice plate comprises an inner assembly and an outerassembly surrounding the inner assembly, wherein the first and/or secondsensor is embedded on an inner assembly of the orifice plate.

In another embodiment, the controller determines a flow coefficientbased on the position of the inner and outer assemblies, further whereinthe flow coefficient is determined based on a calculation or a look-uptable. It is contemplated that the flow coefficient is a non-constantcoefficient. In some aspects, the look-up table comprises empirical testdata. In another aspect, the controller determines a flow rate based onthe pressure differential and a flow coefficient, wherein the flowcoefficient is determined theoretically as a function of a ratio of avariable opening area and a duct area. In a further aspect, thecontroller determines a flow rate further based on a flow coefficientthat is applied at a maximum fluid flow to determine a maximum flow ratefor use in calibration.

Still, in other embodiments, the controller compares the flow rate to atarget flow that may be based on a desired temperature setting andoperates the actuator assembly to maintain or change the variableopening area defined by the inner and outer assemblies based on thecomparison. The controller outputs the flow rate to a central controllerat a central system that supplies the fluid flow to the flow device. Thecontroller may further output the flow rate to at least one of acloud-based system and a BAS (building automation system), and/or theoutput the pressure differential to a room or local controller to managea total flow in and out of a single room or laboratory. Still, in otheraspects, the controller signals a variable frequency driver (VFD) or amotor of an air movement device to effect control of the air movementdevice. The controller may operate other air flow movement devicesplaced downstream or upstream of the orifice plate, further wherein thecontroller operates a motor of the air flow movement device based on apressure differential. In some aspects, the air flow movement devicecomprises one or more fans. In another aspect, the controller regulatesthe variable opening based in part on a turndown ratio defined by amaximum volume of fluid flow through the orifice plate to a minimumvolume of controllable fluid flow through the orifice plate, wherein theturndown ratio greater than 10:1. The turndown ratio, also known as arangeability of the controller, may be greater than 100:1, and/or be amember selected from the group consisting of 25:1, 50:1, 75:1, 100:1,125:1, 150:1, 175:1, 200:1, 225:1, 250:1, 275:1, and 300:1. In aparticular aspect, the turndown ratio is between about 25:1 to about300:1. Furthermore, the flow device is self-commissioning based on theturndown ratio.

In some embodiments, the controller is a single microelectroniccontroller in communication with a plurality of room sensors in aplurality of room zones to control the plurality of room zones. Thecontroller operates the fluid device such that the HVAC system meets atleast one prevailing energy code selected from a group consisting ofASHRAE Standard 55-2010, ASHRAE Standard 62.1-2010, ASHRAE Standard90.1-2010, ASHRAE Standard 62.2-2010, ASHRAE Standard 90.1-2010,California Title 24, and CAL Green. At least one of the orifice plateand the actuator assembly are in communicative operation with anotherair distribution device selected from a group consisting of fan-powereddevices, air handlers, chilled beams, VAV diffusers, unit ventilators,lights, fire or smoke dampers, control dampers, control valves, pumps,chillers, Direct Expansion Evaporative cooled air conditioning packageunits, and pre-piped hydronics. Furthermore, the flow device may be incommunication or equipped with at least one ancillary component selectedfrom a group consisting of controls, sensors, firmware, software,algorithms, air moving devices, fluid moving devices, motors, andvariable frequency drives (VFDs). Even further, the flow device is incommunication or equipped with additional linkages, gears or specialactuators to turn additional concentric tubes, dampers, valves or rodsto optimize air flow measurement performance. In yet another aspect, theflow device is configured with or as a multiple outlet plenum with twoor more fluid device assemblies, wherein the multiple outlet plenumpermits multiple accurate room or zone control of multiple rooms orzones simultaneously with at least member selected from a groupconsisting of a single self-contained BTUH generating device, a multiplethermal transfer device, an air to air HVAC system, and a fluid basedsystem.

In other embodiments, the flow device is provided in combination with 5to 180 degree symmetrical or flow-straightening elbows defining at leasta portion of the flow pathway upstream or downstream of the orificeplate, wherein the elbows adapt the device to tight space constraints.In an alternative embodiment, a plurality of venturi or orifice valvesof different sizes are ganged together to simulate multiple variableventuri flow measurement. In another aspect, the flow device includes adouble-duct housing having two or more different sized inner and outerassemblies to replicate a two-stage assembly. The flow device mayfurther be in combination with at least one thermal transfer unitinstalled upstream or downstream of the device where the duct is larger,thereby increasing a heat transfer surface and allowing for at least oneof a member selected from a group consisting of a lower air pressuredrop, a lower water pressure drop, a localized heating and cooling, are-setting chiller, a re-setting boiler, and a reduced pump horsepower.In yet another aspect, the device is housed in or in communication withat least one member selected from a group consisting of a variable airvolume (VAV) diffuser, a grill diffuser, and a linear diffuser. The VAVdiffuser may be wireless or hardwired with the flow device and may usevarious means of actuation such as gear, cable, rotors. Can becontrolled from smart devices such as mobile devices and tablets

In still other embodiments, the fluid flow downstream of the orificeplate is discharged directly into an ambient space of a room. The flowdevice may include an all-inclusive light.

Still further, at least one of the all-inclusive light and an HVACdiffuser are controlled by one onboard controller. In yet anotheraspect, the flow device further comprises or is in communication with abuilt-in occupancy sensor, wherein the sensor is selected from a groupincluding an infrared sensor, a motion sensor, an ultrasonic sensor, atemperature sensor, a carbon dioxide sensor, a humidity sensor, andsmart camera with occupant tracking capability. The flow device is inoperative communication or housed in a smart self-balancing airdistribution (SBAD) adjustable diffuser having a temperature sensor,further wherein the operative communication is wireless or hardwired. Insome aspects, the flow device is in operative communication or housed ina smart self-balancing air distribution (SBAD) motorized diffuser.

In still further embodiments of the present disclosure, a controller isprovided that is in communication with a damper assembly and configuredto measure fluid flow through a flow pathway. The controller comprises aprocessor and a memory communicatively coupled with and readable by theprocessor and having stored therein processor-readable instructionsthat, when executed by the processor, cause the processor to determineat least one of the following: 1) a pressure differential based on afirst pressure sensed upstream of the damper assembly and a secondpressure sensed downstream of the damper assembly, wherein the damperassembly is disposed in the flow pathway; 2) a variable opening areadefined by the damper assembly, wherein the variable opening areareceives the fluid flow there through; 3) a flow coefficient MF based ona function of a ratio of the variable opening area to a flow pathwayarea, wherein the flow coefficient M_(F) is 0≥M_(F)≤1; and 4) a flowrate based on the pressure differential and the flow coefficient.

It is contemplated that the processor further controls a flow velocityor feet per minute of the fluid flow while varying a flow rate or cubicfeet per minute of the fluid flow throughout an entire turndown rangedefined by the processor. The flow rate is further based on a flowcoefficient that is applied at a maximum fluid flow to determine amaximum flow rate, wherein the maximum flow rate is used for calibrationpurposes. The controller may. incorporate the required pressuretransducer.

In other aspects, the controller controls the variable opening area ofthe damper assembly and the processor-readable instructions areprogrammed for optimal performance, acoustics, and energy of thecontroller and the controlled damper assembly. The controller may be incommunication with at least one of a cloud-based control computing andwireless control components. In still other aspects, the controller isfurther monitored and controlled by building automation system (BAS)software of a BAS system. The controller further balances the damperassembly in real time from a front end software building automationsystem (BAS). Merely by way of example, the real-time balancing data isdisplayed at a member selected from a group comprising a front endsoftware BAS system, a controller installed on self-containedcompressor, a fluid moving device, and a room air discharge device toallow the moving device to be controlled and interface with anotherequipment controller.

In yet another aspect, the controller provides real-time turn downcapabilities of a fluid moving device in operative communication withthe damper assembly. The controller may include processor-readableinstructions that further comprise an algorithm based on calculatingfluid through orifices. The algorithm may be based on at least onemember selected from a group consisting of an orifice metering device, afluid sensing element, an actuator resolution, and a transducer.Furthermore, the controller automatically calculates the flowcoefficient M_(F) based on the variable opening area. The flowcoefficient M_(F) calculation is performed with a turndown ratio of 10:1or greater. In other aspects, the controller determines the flow ratebased on multiplying the flow coefficient M_(F) with a square root ofthe determined pressure differential and then scaling to read mass fluidflows in desirable engineering units.

In still another embodiment of the present disclosure, an actuatorassembly in operative communication with a damper assembly that isconfigured to measure and control fluid flow through a flow pathwaycomprises a first actuator in communication with a first gearing.

The first gearing is adapted to receive at least one of a first andsecond shaft extending from at least one of an inner and an outerassembly of the damper assembly.

In some aspects, the first gearing comprises a dual concentric output torotate the inner and outer assemblies. The first gearing comprises aninner track operatively coupled with the first shaft and an outer trackoperatively coupled with the second shaft. Furthermore, a secondactuator is provided in communication with the first actuator, whereinthe first actuator is operatively connected to the first shaft and thesecond actuator is operatively connected to the second shaft. The firstand second actuators may be ganged together. At least one of the firstand second actuators is in wireless communication with a controller thatoperates the actuator assembly. In still another aspect, the actuatorassembly outputs feedback from at least one of the first and secondactuators. In other embodiments, at least one of the first and secondactuators is removably received on a mounting bracket that is adapted toengage an outer surface of a housing of the damper assembly. Anotheractuator uses one motor with gear drives to drive both the shafts.Another actuator can use cranks and/or a camrace to drive both theshafts. A feedback signal can be accomplished by using a potentiometer.

In yet another embodiment of the present disclosure, a flow device formeasuring fluid flow through a flow pathway comprises a damper assemblydisposed in the flow pathway, wherein the damper assembly comprises arotary damper plate positioned within the flow pathway and defining atleast a portion of a variable opening. The flow device further comprisesan actuator assembly operatively connected with the damper assembly anda controller in operative communication with the damper assembly,wherein the controller comprises a processor and a memorycommunicatively coupled with and readable by the processor and havingstored therein processor-readable instructions that, when executed bythe processor, cause the processor to determine at least one of thefollowing: 1) a pressure differential based on a first pressure sensedupstream of the damper assembly and a second pressure sensed downstreamof the damper assembly; 2) a variable opening area based on a positionof the damper plate; 3) a flow coefficient M_(F) based on a function ofa a ratio of the variable opening area to a flow pathway area, whereinthe flow coefficient M_(F) satisfies 0≤M_(F)≤1; and 4) a flow rate basedon the pressure differential and the flow coefficient.

In some aspects, the flow pathway is defined by a housing having ahollow inner surface configured to removably receive the damper assemblyand an opposing outer surface configured to removably mount the actuatorassembly thereon. The housing may include a Venturi valve defining aconstriction section for the flow pathway. In other aspects, the housingfurther defines a door or plate covering an opening in the housing,wherein the opening permits access to the damper assembly in the housingfor maintenance cleaning and replacement of parts.

The damper assembly may be a butterfly damper and the variable openingis defined between the damper plate and a surface defining the flowpathway. The butterfly damper includes a primary damper that issubstantially circular or rectangular and the variable opening is acontrollable opening that enables measurability and controllability overa wide flow range. In some aspects, the controllable opening issubstantially circular or rectangular. The controllable opening may be asliding or guillotine-type opening. Further, the primary damper may be asliding or guillotine-type damper. In another aspect, the primary damperfurther includes regain fittings enabling measurability andcontrollability over a wide flow range. The regain fittings comprise atleast one of a fairing placed upstream of the primary damper and anacelle placed downstream of the primary damper.

The damper assembly may be a 2-stage damper assembly comprising acentral opening in the damper plate and an inner rotary disk extendingthrough the central opening to define the variable opening. The damperplate and the inner disk overlap to define an overlap region that mayinclude a compressible gasket embedded on at least one of the damperplate and the inner disk. A plurality of damper assemblies may beprovided in series or in parallel in the flow pathway and the pressuredifferential may be determined based on a first pressure sensed upstreamof the damper assemblies and a second pressure sensed downstream of thedamper assemblies. In another aspect, the controller determines a newposition setting for the damper assembly based on the flow rate andsignals the actuator assembly to adjust the damper assembly to the newposition. The controller may output at least one of the pressuredifferential, the variable opening area, the flow coefficient, and theflow rate to an external controller in communication with anothercontroller. Further, the actuator assembly may further comprise anelectro-mechanical or pneumatic mechanical device.

In yet another embodiment of the present disclosure, a method isprovided for controlling fluid flow through a duct defining across-sectional area A_(d). The method includes the step of providing acontrol element in the duct, wherein the control element defines avariable opening area A_(o) that amplifies a velocity pressure of thefluid flow through the control element. The method further includesmeasuring a pressure differential ΔP across the control element,determining a flow coefficient M_(F) based on a function of a ratioA_(O)/A_(d), and determining a flow rate Q based on a product of theflow coefficient M_(F), the duct area A_(d), and a square root of thepressure differential ΔP. Further, the method may include comparing theflow rate Q to a predetermined target flow F. If Q=F, the methodincludes the step of maintaining a setting of the control elementdefining the variable opening area Ao. If Q≠F, the method includes thestep of performing at least one of: 1) adjusting the setting of thecontrol element to a new setting defining the variable opening areaA_(O); 2) notifying a central controller of a central system thatsupplies the fluid flow to the control element to increase or reduce thefluid flow; and 3) controlling a speed of a fan disposed upstream ordownstream of the control element based on the pressure differential ΔP,damper % open, and/or state of satisfaction of downstream requirements.

The method may further include the step of checking if the predeterminedtarget flow F has changed, wherein if the target flow F has not changedand Q≠F, signaling an actuator to adjust the control element to the newsetting. Further, the method comprises providing a plurality of controlelements in series or in parallel in the flow pathway, measuring thepressure differential ΔP across the plurality of control elements, anddetermining the flow coefficient M_(F) based on the variable openingarea A_(O) of a critical control element in the plurality of controlelements. Still further, the method includes enhancing or magnifying themeasured pressure differential ΔP across the control element andcalculating the flow rate Q based on the enhanced or magnified pressuredifferential ΔP along with the flow coefficient to achieve a preciseflow rate Q. In some embodiments, the control element is a thin bladecontrol element and the pressure differential ΔP is measured across theblade to enhance readings.

In further embodiments of the present disclosure, a flow device formeasuring and controlling a fluid flow through a flow pathway in a ductof a heating, ventilation, and air conditioning (HVAC) system is shown.The flow device comprises an orifice plate positioned within the flowpathway and defining a variable opening for receiving flow therethrough. The orifice plate comprises an outer assembly comprising agenerally central opening and an inner assembly extending through thecentral opening. Further, the flow device includes an actuator assemblyoperatively connected with the orifice plate, a first sensor disposed inthe flow pathway upstream of, and a second sensor downstream of, theorifice plate, and a controller in operative communication with theorifice plate. The controller comprises a processor and a memorycommunicatively coupled with and readable by the processor and havingstored therein processor-readable instructions that, when executed bythe processor, cause the processor to perform at least one of: 1)determine a pressure differential based on a first pressure obtainedbetween the first and second sensors; 2) determine a position of theouter and inner assemblies based on a position feedback received fromthe actuator assembly; and 3) regulate the variable opening based on thepressure differential the position of the outer and inner assemblies.

In yet another embodiment of the present disclosure, a central controlsystem for use in a heating, ventilation, and air conditioning (HVAC)system is provided. The central controls system includes a processor anda memory communicatively coupled with and readable by the processor andhaving stored therein processor-readable instructions that, whenexecuted by the processor, cause the processor to receive data from aplurality of flow controllers, wherein each of the plurality of flowcontrollers operates a flow device positioned remotely from the centralcontrols system. The data may comprise a pressure differential measuredat each of the plurality of flow controllers, a variable opening area ofa flow pathway provided by each flow device, a flow coefficient M_(F)based on square of a ratio of the variable opening area to a flowpathway area at each of the plurality of flow devices, wherein the flowcoefficient M_(F) is a non-constant coefficient and 0≤M_(F)≤1, and/or aflow rate based on the pressure differential and the flow coefficient.The central controller may adjust fan parameters such that 1) all remotecontrollers are satisfied and 2) at least one remote control device iswide open, thus optimizing energy consumption. The central controlsystem may further send operation parameters to each of the plurality offlow controllers independently. If one or more remote controllers isunsatisfied (i.e. wide open and needing more flow), and fan is atmaximum, central control may command satisfied or more nearly satisfiedcontrollers to feather back to balance the load, based on degree ofdissatisfaction reported by remote controllers.

Other operation parameters may include duct and/or zone CFM measurementsfor the purposes of balancing and meeting fresh air requirements.Furthermore, the central control system may adjust a volume of a supplyfluid flow to at least a portion of the plurality of flow devices basedon the data received. In some embodiments, the central processor is inwireless communication with the plurality of flow controllers. The datamay be stored in real-time as it is collected by and sent from each ofthe plurality of flow controllers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front perspective view of a flow device according to variousembodiments of the present invention;

FIG. 2A is a side perspective view of a damper assembly having aplurality of nested dampers;

FIG. 2B is a side perspective view of a damper assembly having arectangular outer damper and a plurality of nested dampers;

FIG. 2C is a front view of a damper assembly having different geometricform;

FIG. 2D is a front perspective view of a damper assembly having anothergeometric form;

FIG. 2E is a cross-sectional view of one of generally a number ofguillotine-damper assemblies in regain nacelles which may be disposedacross a generally rectangular duct, according to some embodiments ofthe present disclosure;

FIG. 2F is a cross-sectional view of another guillotine-damper assemblyin a regain nacelle, according to some embodiments of the presentdisclosure;

FIG. 3A is a schematic diagram of a camrace in a single gear for a onepiece actuator that drives two damper shafts according to variousembodiments of the present invention;

FIG. 3B is a schematic of a linear actuated cam-driven airvalve inaccordance with an embodiment of the invention;

FIG. 3C is a schematic of a rotary actuated cam-driven airvalve inaccordance with an embodiment of the invention;

FIG. 3D is schematic representation of a crank actuated shaft with anactuator in a general position;

FIG. 3E is schematic representation of a crank actuated shaft with anactuator in both open and closed position, as well as at theintermediate position of maximum leverage;

FIG. 3F is a graph representing the flow coefficient relative toactuator position when using cam races as disclosed herein;

FIG. 3G is a graph representing the blade position relative to actuatorposition when using cam races as disclosed herein;

FIG. 3H is a graph representing the flow coefficient relative toactuator position when using other means of actuation;

FIG. 3I is a graph representing the blade position relative to actuatorposition when using other means of actuation;

FIG. 4A is a schematic diagram of a damper assembly attached to a gearbox and actuator according to various embodiments of the presentinvention;

FIG. 4B is a side view of a drive gear and driven gear according tovarious embodiments of the present invention;

FIG. 5A is a front perspective view of the flow device of FIG. 1 withina housing;

FIG. 5B is a front angled view of FIG. 5A;

FIG. 5C is a back angled view of FIG. 5A;

FIG. 6A is an angled perspective view of a Venturi valve having the flowdevice of FIG. 1;

FIG. 6B is a front angled view of FIG. 6A;

FIG. 7A is a side view of a circular housing having the flow device ofFIG. 1;

FIG. 7B is a front perspective view of FIG. 7A;

FIG. 7C is a phantom view of FIG. 7A;

FIG. 7D is a front perspective view of a rectangular 2 stage damper;

FIG. 8 is a schematic diagram of a controller and network according tovarious embodiments of the present invention;

FIG. 9 is a flow diagram of a method according to various embodiments ofthe present invention;

FIG. 10A illustrates an SBAD adjustable diffuser with temperaturesensing, according to various embodiments of the present invention;

FIG. 10B illustrates an SBAD motorized diffuser;

FIG. 10C illustrate an SBAD diffuser damper;

FIG. 11 shows a schematic diagram of a controller or computer device;

FIG. 12 depicts aspects of low flow fluid control systems and methodsaccording to embodiments of the present invention;

FIG. 13A is a perspective view an embodiment of a damper assembly havinga plurality of horizontal blades;

FIG. 13B is a frontal view of the damper assembly shown in FIG. 13A;

FIG. 13C is a right side view of the damper assembly shown in FIG. 13;

FIG. 13D is a left side view of the damper assembly shown is FIG. 13A;

FIG. 14 is a perspective view of another embodiment of a damper assemblyhaving a plurality of horizontal blades;

FIG. 15A is a perspective view of another embodiment of a damperassembly having a plurality of horizontal blades;

FIG. 15B is a left side view of the damper assembly shown is FIG. 15A;

FIG. 16A is a perspective view of another embodiment of a damperassembly having a plurality of horizontal blades;

FIG. 16B is a frontal view of the damper assembly shown in FIG. 16A;

FIG. 17A is a perspective view of a reheat box with a blade damperassembly incorporated therein;

FIG. 17B is a top view of the reheat box shown with a butterfly damperassembly incorporated therein;

FIG. 18A shows a schematic view of an Orifice plate in InfiniteReservoir;

FIG. 18B is a graph of Scaled v² Correction Term f(2+f);

FIG. 18C is a graph of a Flow Correlation Factor f;

FIG. 18D is a schematic view of a Ducted Orifice Plate;

FIG. 18E is a graph of Radial Velocity on Orifice Plate;

FIG. 18F is a graph of Integrands of Ducted vs. Infinite Plate;

FIG. 18G is a schematic view of a Butterfly Damper;

FIG. 18H is a graph of a Butterfly Damper Open Area;

FIG. 18I is a schematic view of initial airflow through a ButterflyDamper with an Annular Gasket;

FIG. 18J is a schematic view of airflow at the initial opening through a2-Stage Damper;

FIG. 18K is a schematic view of the inner disk showing gasketingoptions;

FIG. 18L is a graph of a simplified model for the Flow Coefficient of a2-Stage Damper;

FIG. 18M is a detailed side view of the initial opening parameters for adamper with duct wall gasket

FIG. 18N is a detailed face view of the initial opening parameters for adamper with duct wall gasket

FIG. 18O is a detailed side view of the initial opening parameters forthe inner disk of a 2 stage damper

FIG. 18P is a detailed face view of the initial opening parameters forthe inner disk of a 2 stage damper

FIG. 19A is a perspective view of an air distribution apparatus inaccordance with another embodiment of the present invention;

FIG. 19B is a detailed perspective view of some components of the airdistribution apparatus shown in FIG. 19A;

FIG. 19C is a lever rod square shown in FIG. 19B;

FIG. 19D hinge plate shown in FIG. 19B;

FIG. 19E is a perspective view of a air distribution apparatus inaccordance with another embodiment of the present invention;

FIG. 19F is a partial front view of the air distribution apparatus shownin FIG. 19E with a rotary actuator;

FIG. 19G is a detailed view of an embodiment of a linear actuator for anair distribution apparatus; and

FIG. 19H is a detailed view of another embodiment of a linear actuatorfor an air distribution apparatus.

DETAILED DESCRIPTION OF THE INVENTION

The present disclosure describes a flow device, also referred to as afluid control measuring device or a low flow fluid controller (“LFFC”)that offers a high turndown ratio for measuring and regulating varioustypes of fluid flow, such as gaseous or liquid fluid flows having highor low velocity. It is noted that although the term LFFC may be usedthroughout the application, the flow device is applicable to a varietyof fluid flows and is not limited to low flow. The LFFC can beincorporated into a duct, a self-contained heating, ventilation, and airconditioning (“HVAC”) equipment, or any air or fluid discharge ordistribution device. Further, the LFFC is a smart device capable ofinteracting with other devices through a variety of networks, includingBluetooth, WiFi, 3G, 4G, and the like.

In some embodiments, the LFFC is a circular plate-like device thatincludes one or more damper regulators and/or fluid control valvesmounted in series and/or parallel in a flow pathway. The dampers andvalves may be housed or un-housed in a tube or other geometric housingdefining a portion of the flow pathway. Numerous other geometricconfigurations and materials for the LFFC may be utilized, as describedbelow.

In practice, the LFFC may be implemented in conjunction with a method ofcontrol that applies the Flow and Discharge Coefficient Correlations.This method provides a comprehensive orifice plate model thatcontributes to the high turndown ratio and facilitates the LFFC tomeasure or regulate very low volumes of fluid flow with precisioninexpensively. Further, the LFFC offers superior acoustics by greatlyreducing noise generation and eliminating the need for sound-attenuatingliners such as fiberglass, double wall, armor flex, and the likeEliminating such sound-attenuating components may reduce pressure dropof the fluid flow and contribute to energy savings.

Overview of Benefits of the LFFC

The LFFC described herein provides a practical means for measuring fluidflow, particularly low air and fluid volumes, and regulating theresulting flows. In practice, implementation of the LFFC in an HVACbuilding system offers building operators more options to provide freshair to occupants, while meeting new energy standards and providing highzone controllability. The LFFC described herein simplifies current HVACsystem designs. In this way, the LFFC eliminates or reduces prior needsfor a plurality of device sizes in building construction. Furthermore,the LFFC allows for self-balancing and continuous commissioning ofsystems.

In another aspect, the high turndown ratio of the LFFC enablesstreamlining product portfolios by combining many product part numbersinto a much smaller number of offerings, sometimes as much as 10,000 ormore part numbers. In this way, the LFFC reduces manufacturing costs,engineering time, cataloguing, engineering documentation, drawings,acoustical calculations, and the like. It is further contemplated thatin doing so, complex software programs are not required, therebyreducing overhead and mistakes for customers, manufacturers and saleschannels. In addition, a streamlined product offering allows for moresensors, hardware, software and firmware to be installed on devices atlow incremental cost, thus enhancing product technology and systemintegration.

In some embodiments described herein, the LFFC allows for a substantialreduction in fluid pressure of HVAC/process systems, which substantiallyreduces energy requirements. Furthermore, the LFFC redefines the currentcontrols firmware/software architectures by making cloud computing ofbuilding control networks feasible and continuous commissioning ofbuildings applicable in an inexpensive manner. The LFFC has applicationsin multiple types of existing products, such as air distributiondevices, air valves, fan coils, air handlers, thermal transfer devicesusing fluid, electric, chemical, gas, nano-fluid, process equipment aswell as hybrid products that combine several existing products into one,while both encompassing mechanical systems and controls networkarchitectures, software and firmware.

In further aspects, the LFFC may be introduced for new and retrofitconstruction into HVAC building equipment (commercial, residential andindustrial), as well as other implementations such as burner and boilerequipment. For instance, the LFFC may be sized to those of existingvalves for quick retrofit into existing installations. In anotheraspect, the LFFC may entail only two or three LFFC sizes for a newconstruction.

The LFFC is also applicable in residential settings, oil refineries,industrial, pharmaceutical, and process markets, and may be utilized forair and water, with direct expansion into hybrid electric reheat orother types of thermal conductivity, including nuclear, chemical andelectrical. In a particular aspect, the LFFC may be incorporated intocentral systems and zone systems of building HVAC equipment. Centralsystems equipment tend to be large, while zone systems equipment tend tobe located at the room level and sold in larger quantities. It iscontemplated that the LFFC may replace or displace existing variable airvolume (“VAV”) terminal control boxes in zone systems, which areubiquitous throughout buildings today. The LFFC may also be used onlarge systems, including air handlers/package rooftop units and otherancillary products in a HVAC system in a building. Even further, theLFFC can be used in fluid-based systems, such as variable refrigerantsystems, chilled beams and in under floor applications and/or hybridsystems. In addition, the LFFC facilitates hybrid systems utilizingwater and gas to become more feasible, including facilitating the use ofnano-fluids and heat pipes in low static pressure systems.

Merely by way of example, the LFFC can be incorporated into under floordesign and chilled beams to accurately measure or control primary airinto the child beams. This optimizes the heat coefficient of chilledwater coils commensurate with system requirements, occupant comfort, andzone performance. The LFFC can also be used on a device that heats orcools with a single controller, maintaining a set point within severalseparate zones simultaneously. In this way, chilled beams can bereplaced altogether. Furthermore, doing so may replace fan-powered boxesand fan coils or small AHUs. In another aspect, the LFFC can be coupledwith next-generation, smart “Lego” systems, thereby reducinginstallation costs by about 50% and utilizing energy savings of localwater-based or refrigerant-based heating and cooling.

In another example, the LFFC can be used in fan coils and small AHUs.Legacy fan coils utilize high pressure drops through the coils, filters,and the like, to achieve a sufficiently compact foot print.Incorporation of the LFFC allows for mixing and matching of ancillarycomponents in various geometric shapes and sizes. This may reduce spacerequirements, pressure drops, and deliver superior occupant comfort tovarious zones simultaneously, exactly per each zone's set point. Evenfurther, product portfolios may be streamlined since the same portfoliomay be applied to multiple vertical channels. In another aspect, theLFFC may provide a new device that replaces horizontal fan coils.

In still another example, the LFFC can provide new dampers, since theLFFC has lower pressure drops and improved air flow measurement atsubstantially less cost than existing damper technology. It iscontemplated that various streamlined damper designs can be used withthe LFFC to permit the LFFC to support various applications, such aspackaged rooftop units, variable refrigerant flow (“VRF”) applications,air handling units (“AHUs”), and the like. The LFFC can also be used oneconomizers and/or high humidity applications. Further, the LFFC can beincorporated in smart self-balancing air distribution (“SBAD”) devices,which may use wireless technology and communicate directly with anequipment controller. Incorporation of the LFFC in SBAD devices can alsoyield pressure independent, pressure dependent, or hybrid devices. Inyet another example, the LFFC may be incorporated residential marketswith multiple outlet plenum designs to feed multiple zones and reduceequipment load requirements.

The high turndown LFFC makes it possible to more precisely measure airand water volumes to guarantee compliance with fresh air standards,while not breaking the energy bank. The key to improved LFFC operationis a high turndown ratio. Merely by way of example, current devicesoperate with 4 to 5-1 turndown ratio. The LFFC, by design and/orunlocking software code related to the functionality of the LFFC, canoperate with a turndown ratio that can be increased to 100-1 or 200-1,or even higher. Reliable low flow data from the terminals allows centralfans and pumps to be controlled by supply requirements at the neediestterminal device rather than by the energetically wasteful fixed pressurein the supply duct. Dissipation of excess pressure is responsible forexcessive noise generation in the terminal devices. Moreover, a higherturndown ratio results in a streamlined product portfolio and/or aconsolidation of several product portfolios into one. This results inreduced manufacturing costs, installation costs and lower life cyclecosts for the building.

Merely by way of example, the high turndown ratio allows the LFFC to beshipped more easily at an earlier time frame to the job site. The highturndown frequently allows a single part number to cover requirements ofan entire system, which allows for shipping the product earlier anddecreasing the time to completion of a building. According to someembodiments, the LFFC can provide a single approach that is universallyapplicable for many HVAC designs, rather than having one design for eachoperating range. In today's fast-paced construction business, shipmentlead times are a major factor into the construction cycle planning andtiming. By reducing the number of product variations and/or making oneproduct cover a much larger dynamic operating range, building architectsand engineers are freed up to focus on the overall project and thedetails of the design. Incorporation of the LFFC allows for phasing ofshipments later in the construction cycle without having to deal withdifficulties about whether the air moving and/or water controllingequipment will still work after all the last minute changes are made bythe building owner.

In another example, the high turndown LFFC allows the LFFC and anyancillary components to have lower pressure drops, which further reducesfan horsepower and energy consumption. In practice, this may aid inachieving optimized performance of variable frequency drives (“VFDs”)and electrically commutated motors or solid state motors. The LFFCfurther facilitates lowering condenser water temperature, which lends toenergy savings utilizing condensing boilers, heat recovery etc. Inanother aspect, the LFFC allows for hot reheat temperatures to bereduced to 95-105° F. (37-40° C.) with higher delta temperatures andreduced GPM (gallons per minute) or LPM (liters per minute). In anotherrespect, the LFFC allow for chilled water temperatures to be increasedwith higher delta T's thus making the chillers more efficient. In thatcase, pump horsepower may be reduced and efficient utilization of heatrecovery, heat pump chillers, condensing boilers and optimum zonecontrollability may be realized. In yet a further aspect, the LFFCprovides high turndown and accurate flow measurement for localizedchilled water coil optimization design or performance. In anotherrespect, the LFFC allows the BTUHs and fluids to be shifted to occupiedzones as required and setting unoccupied zones to the minimums, thussaving additional energy.

It is noted that the LFFC air valve or damper described herein can bebuilt/designed in countless geometric shapes/sizes, various materials,with several air flow sensors and actuators. The dampers can beinstalled in various geometric angles and various damper assemblies andlinkages. The devices can be designed and manufactured with innumerableturndown ratios and numerous actuator/controls options. Furthermore,there are several variations of damper designs, such as designs moreconducive for stand-alone dampers and equipment such as large airhandlers and packaged roof top units.

In this way, it is contemplated that the LFFC disclosed herein providesat least the following: 1) Measurement and regulation of high and verylow volumes of air and/or fluid flows with precision, inexpensively andwith superior acoustics and requiring less energy; 2) A high turndowndevice that permits use at lower velocities, greatly reducing noisegeneration and eliminating the need for sound-attenuating liners such asfiberglass and double walls; 3) A high rangeability device that allowsstreamlining product portfolios by combining several product partnumbers into much smaller number of offerings; 4) An inexpensive devicethat allows equipment to be scaled back 100-1 or higher, rather than thelegacy 4 to 5-1, which leads to energy savings, fewer product variationssimpler and more robust application designs; 5) A device that providesbetter fluid, air volume and water temperature control, while conservingmore energy, employing a fundamentally simpler design and meeting allnew and old building fresh air, comfort and energy codes; and 6) Adevice that can be engineered, selected, and sized without sophisticatedsoftware programs.

Components of the LFFC

Turning now to FIG. 1, one embodiment of a flow device or LFFC 100 isillustrated. In general, the LFFC 100 comprises a damper assembly 102operatively connected with an actuator assembly 104 through one or morerotating shafts. The damper assembly 102 is adapted to be positionedwithin a fluid flow pathway of a duct. The damper assembly 102 functionsas an orifice plate that defines a variable opening 106 for receivingfluid flow there through to measure and control various types of air,gaseous, and liquid fluid flow. In a particular aspect, the damperassembly 102 permits measurement and control of very low flow that arenot measurable or controllable by conventional technology. Merely by wayof example, such flows may be 11 cubic feet per minute (CFM) or lower.Further, the LFFC 100 may be a standalone device for measuring andcontrolling fluid flow.

As shown in FIG. 1, the damper assembly 102 is a two-stage assembly thatincludes an outer damper 108 having a central opening 110 and an innerdamper 112 extending through the central opening 110. The outer andinner dampers 108,112 are generally thin, flat rotary plates that rotaterelative to each other about a common rotational axis R to vary anopening size, or a variable opening area A_(o), of the variable opening106. In particular, the damper assembly 102 defines the variable openingarea A_(o) by the position of the outer and inner dampers 108,112relative to one another. Such positioning may include different anglesor offset distances defined between the dampers 108,112. In this way,the variable opening area A_(o) may be a summation of one or more holesin the damper assembly 102 where fluid flows through. For instance, FIG.1 shows two passageways A1 and A2 defined by the damper assembly 102that contribute to the total variable opening area A_(o). In anotheraspect, the variable opening 106 comprises a plurality of additionalopenings that are arranged in parallel.

Rotation of the damper assembly 102 is driven by the actuator assembly112 through one or more shafts. In the embodiment of FIG. 1, tworotating shafts are provided with one shaft corresponding to each of thetwo dampers 108,112. A hollow outer shaft 114 extends from the outerdamper 108 along the rotational axis R to the actuator assembly 112. Aninner shaft 116 extends from the inner damper 112 and through the hollowouter shaft 114 along the same rotational axis R. The inner shaft 116may be solid or hollow and in operative communication with the actuatorassembly 112. The outer and inner shafts 114,116 are driven by theactuator assembly 104 to rotate relative to one another to alter thevariable opening area A_(o) for measurement and control of various typesof fluid flow. It is contemplated that the damper 15 assembly 102 and/orshafts 114,116 can be formed from a variety of materials, includingcarbon fiber, 316 steel, injection molded elements, and other materialsor combinations thereof. The dampers 108,112 can be sized according to asize of the flow pathway or cross-sectional duct area A_(d) defining theflow pathway. In one aspect, the inner damper 112 is sized correspondingto the central opening 110 of the outer damper 108. Merely by way ofexample, the outer damper 108 is about 10 inches in diameter and thenested inner damper is about 3.5 inches in diameter.

As shown in FIG. 1, the outer damper 108 is circular or ring-shaped andthe inner damper 112 is a circular, non-perforated solid disk. The outerand inner dampers 108,112 are nested together. It is noted that othergeometric forms and configurations can be provided, as illustrated inFIGS. 2A-D. For instance, FIG. 2A illustrates a three-stage damperassembly 102 a comprising an outer damper 108 a, an inner damper 112 a,and an intermediary damper 118 nested therebetween. The three dampers108 a, 112 a, 118 rotate relative to one another and/or independently,and/or are driven independently, about the common rotational axis R. Theintermediary damper 118 is ring-shaped in similar fashion to the outerdamper 108 such that the 30 intermediary damper 118 defines anadditional opening 120 that receives the inner damper 112 atherethrough. It is contemplated that any of the dampers 108 a, 112 a,118 can be provided and in any geometric shape. Single-stage,four-stage, five-stage, and n-stage damper assemblies can becontemplated. Selection of the number and shapes may be dependent onoptimization of the damper assembly 102 a in controlling a particulartype of fluid flow.

Further, it is contemplated that any number of damper plates may beprovided in a nested assembly as shown in FIGS. 1 and 2A or offset fromeach other such that the additional dampers are arranged side-by-sidedown the flow pathway. For instance, the damper assembly 102 a mayinclude an inner damper comprising a plurality of nested dampers,wherein at least one of the plurality of nested dampers comprises anadditional opening. In another aspect, the damper assembly 102 a maydefine an offset distance between one or more neighboring dampersthrough the flow pathway. It is contemplated that each of the pluralityof dampers is operatively connected to a shaft that further connects toan actuator assembly, such as the actuator assembly 104 in FIG. 1. Theshafts may comprise hollow and solid shafts nested concentrically toform a shaft assembly 122, as generally indicated in FIG. 2A. In thisway, each of the plurality of dampers can rotate relative to oneanother. In another aspect, the total variable opening area A is definedby a total area of holes in the damper assembly 102 a where fluid flowsthrough. As shown in FIG. 2A, the total variable opening area A_(o)includes four passageways A₃, A₄, A₅, and A₆.

FIG. 2B illustrates a damper assembly 102 b that is similar to thethree-stage damper assembly 102 a, but with a rectangular outer damper108 b. The outer damper 108 b may be formed in any shape. In anexemplary embodiment, the outer damper 108 b is shaped corresponding toa shape of a flow pathway defined by the duct or housing surrounding theouter damper 108 b. Merely by way of example, as further shown in FIGS.2C-D, various other geometric shapes may be contemplated. FIG. 2Cillustrates an outer damper 108 c having a central opening 110 c that istriangular or trapezoidal in shape. An inner damper 112 c is defines acorresponding triangular or trapezoidal shape. FIG. 2D illustrates anouter damper 108 d having a central opening 110 d that is diamond-shapedand an inner damper 112 d that is correspondingly diamond-shaped. Any ofthe inner, intermediate, and outer dampers can define any combination ofshapes, such as shapes that are generally circle, triangle, diamond,trapezoid, rectangle, ellipsis, and dough-nut shaped. In another aspect,the dampers may be symmetrical, non-symmetrical, and/orirregular-shaped.

Still, in another aspect, the damper assembly 102 is a butterfly dampernested within another butterfly damper (the inner damper 112 nestedwithin the outer damper 108). The variable opening 106 is definedbetween the outer damper 108 and a surface defining the flow pathway, aswell as between the butterfly dampers. The variable opening is acontrollable opening that enables measurability and controllability overa wide flow range. It is contemplated that the controllable opening issubstantially circular or rectangular. In still another aspect, thecontrollable opening is a sliding or guillotine-type opening. Forinstance, the primary damper is a sliding or guillotine-type damper 200.As shown in FIG. 2E, the guillotine-damper 200 may include a pluralityof long, symmetrical parallel wings 204 with slots to accommodate thesolid strips 202 in a movable flat plate containing many long narrowparallel slots. The plate slides so that the solid strips 202 are insidethe wings (or regain nacelles) in a fully open position, and almostfully out sealing the paths in fully closed position.

In another embodiment of the guillotine-type damper, upstreamhalf-cylinders 206 may be attached to, or integral with, a movableplate, such that the half cylinders slide. In another embodiment, it iscontemplated that quarter-cylinder at one wall slides little or not atall, and the one at the other wall extends in a line perpendicular tothe wall which passes into a slotted piece outside the wall as thedamper opens.

Turning back to FIG. 1, the actuator assembly 104 is shown comprising afirst actuator 124 and a second actuator 126. The first and secondactuators 124, 126 are ganged together, collinearly, by a stackingbracket 128 comprising first and second shelves 130, 132 securedtogether by four rods 134, whereby each shelf 130, 132 is adapted toreceive each actuator 124, 126. The actuators 124, 126 may be removedfrom the stacking bracket 128. In another embodiment, the actuators 124,126 are not ganged together or collinear and are arranged separately. Itis contemplated that any number of actuators and/or corresponding numberof shelves can be provided for the LFFC 100 and/or the stacking bracket128. In some embodiments, one actuator is provided for each damper ofthe damper assembly to rotate the dampers independently. For instance,the first actuator 124 may be operatively coupled to the hollow outershaft 114 and the second actuator 126 may be coupled with the innershaft 116.

Referring to FIG. 3A, a dual cam race gear 300 is generally shown. Acircular shaft path 302 illustrates that position of concentric outer114 and inner damper shafts 116 as dual cam race gear 300 rotates. Dualcam race gear 300 comprises an outer damper cam race 304 and an innerdamper cam race 306. In this embodiment, outer damper shaft 114 attachesto cam follower 320 which follows cam race 304 to form a high flow bladeactuation assembly and inner damper shaft 116 attaches to cam follower322 which follows cam race 306 to form a low flow blade actuationassembly. When both the outer damper 108 and inner damper 112 are closedat 0% of stroke, position 308 shown on the shaft path 302, the follower320 is in position A and follower 322 is in position A′. As dual camrace gear 300 rotates clockwise 180 degrees to position 310 on the shaftpath 302 at 50% of stroke, the outer damper 108 remains closed, itsfollower 320 remaining fixed as it follows the outer cam race 304 whichmaintains a fixed radius traveling from A to B, while inner damper 112opens fully, its follower 322 rotating linearly following a centeredtrochoid in the inner camrace 306 from A′ to B′. After dual cam racegear 300 rotates a further 180 degrees to complete its 360 degreestroke, both the outer damper 108 and inner damper 112 are completelyopen at 100% of stroke, position 312, which coincides with initialposition 308, on the shaft path 302; the outer damper follower 320 is inposition C in race 304 while the inner damper follower 322 is inposition C′ in race 306. For sequential linear actuation, inner damperfollower 322 follows a converging centered trochoidal path in race 306from position A′ at 0% to near position B′ at 310, 50% of stroke, thensmoothly joins a circular path concentric with the central axis from alittle after B′ to position C′ at 100% of stroke. Outer damper camfollower 320 follows a circular path from position A to position B at50%, then smoothly joins a centered trochoid from a little afterposition B to position C at 100% open. Dual cam race gear 300 furthercomprises teeth 314 that engage with teeth 316 on a pinion gear 318 thatprovides the driving force to rotate dual cam race gear 300. If thecamstroke were contracted to slightly less than 360 degrees, a rotarypotentiometer 370 could be positioned on dual cam race gear 300 todetect the position (angle) of the outer damper 108 and inner damper 112and provide feedback to any controller. Alternatively, and moreaccurately, rotary potentiometers may be positioned on the damper shaftsthemselves to provide feedback of damper position to any controller.

Referring to FIG. 3B, the linear path of Airvalve concentric outer 114and inner damper 116 shafts are depicted based on a linear actuationalong axis X. Linear, non-concentric, actuation is preferable forparallel blade damper assembly 1300, described below. When both outerdamper 108 and inner damper 112 are closed (0% of stroke) position 334on axis X, the outer damper cam follower 320 is shown at A and the innerdamper 112 cam follower 322 at A′. As the actuation proceeds to the 20%stroke position 336, the outer damper follower 320 is shown at B and theinner damper follower 322 at B′. As the actuation proceeds further alongto the 40% stroke position 338, the outer damper follower 320 is shownat C and the inner damper follower 322 at C′. Finally, as the actuationproceeds to the end at the fully open 100% position 340, thecorresponding positions of the outer follower 320 is shown at D and theinner follower 320 at D′. Constant cam follower position is shown asstraight lines AB and C′D′ parallel to the axis of actuation X, withlinear actuation following trochoids from positions B to D and A′ to C′.It can be seen that outer follower 320 and inner follower 322 rotationrange of 0 degrees to 90 degrees correlates with actuation range of 0%to 100% stroke. Inner damper 112 is fully open at the 90 degree followerposition when actuation is as 40%, and outer damper 108 only begins toopen when actuation passes the 20% position and continues to opencompletely to 90 degrees follower rotation when actuation is at 100%.

Turning to FIG. 3C, the relative positions of outer damper 108 and innerdamper 112 are depicted based on a rotary actuation mechanism. Gearsegment 350 has teeth 352 are driven by corresponding teeth 354 onpinion gear 356. Shaft path 358 depicts the relative positions of outerdamper 108 and inner damper 112 as gear segment 350 is actuated. Whenboth outer damper 108 and inner damper 112 are closed (0% stroke),position 360 on shaft path 358, the outer follower 320 is shown at A andthe inner follower 322 at A′. As the actuation proceeds to the 20%position 362, the outer follower 320 follows a circular path AB and theinner follower 322 begins a centered trochoid A′B′. As the actuationproceeds further along to the 40% position 364, the outer followerbegins a centered trochoid BC and the inner follower completes centeredtrochoid A′B′C′. Finally, as the actuation proceeds to the end at thefully open 100% stroke, position 366, the outer follower 322 completestrochoidal path BCD and the inner follower holds steady on circular pathC′D′. Gear segment 350 rotates around pivot point 368 during itsactuation. If linear actuation is desired, inner damper cam race rotates90 degrees following an expanding centered trochoid from position A′ at0% stroke to fully open at C′, 40% stroke, then remains fully openfollowing a circular arc centered on pivot 368 from position C′ to D′.The outer damper cam follower 320 follows a circular arc from A at 0%stroke to position B at 20% stroke (so no cam follower rotation), thencontinues with linear follower rotation following an expanding centeredtrochoid from position B to position D at 100% stroke. Shaft path 358represent an approximately 75 degree arc between the 0% and 100%positions of dampers 108 and 112. Use of cam races described herein canprevent kinks that typically appear in the flow coefficient actuationcurves other means of damper actuation. Smooth non-linear transfercharacteristics are more easily implemented with either rotary or linearcam race configurations.

As shown in FIG. 3D, a representation of a crank actuated shaft isgenerally shown wherein an actuator 380 is shown in a general position.Crank actuation is non-linear over the 90 degree range of action whereinactuation slope

$\frac{d\;\vartheta}{dx}$varies by a factor of at least √{square root over (2)}, and thisnonlinear transfer function can be incorporated into the a flowcoefficient algorithm with minimal loss of accuracy and control. Shaftrotation ϑ and actuator extension x are related through the Law ofCosines:

$x^{2} = {{r^{2} - {2{ar}\;\cos\;\vartheta} + {a^{2}\mspace{11mu}{or}\mspace{14mu}\vartheta}} = {a\;{\cos\left( {0.5\left( {{\frac{r}{a}\left( {1 - \left( \frac{X}{I} \right)^{2}} \right)} + \frac{a}{r}} \right)} \right.}}}$for crank arm length r and shaft-actuator pivot distance a.

${2x\frac{dx}{d\;\vartheta}} = {2{ar}\;\sin\;\vartheta}$relates actuation slope

$\frac{d\;\vartheta}{dx}$to x and ϑ. The moment arm d is the perpendicular distance from theshaft to the line of actuation, which is an arc of radius r. It can beseen that d=r cos(φ−π/2)=r sin φ. By the Law of Sines,

${\frac{\sin\;\varphi}{a} = \frac{\sin\;\vartheta}{x}},$so

$d = {{\frac{ra}{x}\sin\;\vartheta} = {\frac{dx}{d\;\vartheta}.}}$

Referring to FIG. 3E, actuator 380 is shown in its fully extendedposition. d_(max)=r occurs near the middle of the stroke and d_(min)occurs at one or both endpoints; maximized if at both. This done,

${d_{\min} = \frac{r}{\sqrt{2}}},$so

$\frac{dx}{d\;\vartheta} = d$is √{square root over (2)} times larger near the middle of the strokethan at the endpoints and the actuation slope

$\frac{d\;\vartheta}{dx}$is √{square root over (2)} times bigger at the endpoints than near themiddle of the stroke. This nonlinearity makes the flow coefficientcurves less tractable as functions of stroke x rather than directly interms of ϑ.

${{Actuator}\mspace{14mu}{stroke}} = {{2d} = {\frac{r}{\sqrt{2}}.}}$The shaft actuator pivot distance a=√{square root over (d_(min)²+(d_(min)+x₀)²)}=√{square root over (r²+√{square root over (2)}rx₀+x₀²)}≥r, ≥x₀, and ≤r+x₀, in which x₀ is the contracted actuatorpivot—crank arm attachment length. The actuator pivot 382 is usually butnot necessarily at the opposite end of the actuator from the extensionrod. Those skilled in the art will appreciate that actuation may beaccomplished hydraulically, pneumatically, electrically, thermally ormagnetically.

Referring to FIG. 3F, a graph depicting the slope of a flow coefficientcurve is represented under cam actuation. Compare this to FIG. 3Hshowing slope of the flow coefficient curve under any other form ofactuation When dampers are partially opened, for example, between 0% and30%, the slope is relatively constant, and as the dampers open further,the slope increases. The relatively constant actuation slope allows thecontroller to regulate the HVAV system more tightly with less overshootand undershoot.

Referring now to FIGS. 3G and 3I, graphs depicting the underlyingrelationship between inner and outer damper positions and actuationposition are represented, first under cam actuation, then under anyother form of actuation. The corner rounding and its effect on FIG. 3Gare obvious. Inner damper 112 begins opening immediately under actuationin this simplified model and continues to open linearly to approximately30% actuation. Outer damper 108 begins opening at approximately 15%actuation and continues linearly throughout the actuation range. Lowflow blade or inner damper 108 set opens linearly from 0% stroke throughapproximately 30% of the actuation cycle and is completely openthereafter, with the high flow blade or outer damper 112 opening at aslower rate starting at approximately 15% of the actuation cycle andopening linearly thereafter. This overlap ameliorates (1) a flat regionbetween about 25% and 50% of the actuation cycle that would occur if thehigh flow blade does not begin opening until the low flow blade iscompletely open, both at approximately 50% as can be seen in FIG. in 3A,and (2) a very steep flow coefficient curve as the actuation cycleapproaches 100%. As previously stated, a relatively constant flowcoefficient curve is preferable. This in no way precludes other options,including nonlinear opening characteristics of general character.

Referring to the schematic diagrams in FIG. 4A, the outer and innerdampers 108,112 are attached to a gearbox 400 driven by the remaininggears of the actuator 402. A gearbox 400 can contain any number of gearsto impart appropriate rotation to outer and inner dampers 108,112. In aparticular embodiment shown in FIG. 4A, gearbox 400 includes an outerdamper gear 404 that is adapted to receive the outer shaft 406 connectedto outer damper 108; an inner damper gear 408 adapted to receive theinner shaft 410 of the inner damper 112, and A driving gear 412 that inturn rotates the outer damper gear 404 connected to the outer shaft 406,and subsequently the outer damper 108 in sequence with or overlappingactuation of the inner damper gear 408. In this way, the outer and innerdampers 108,112 can be rotated along the rotational axis R relative toone another by the actuator 402. Actuator 402 employs a shaft 416 thatis attached to gearbox 400 and turns driving gear 412.

In a different aspect, the gearbox 400 may incorporate compound,non-concentric driving and driven gears that may allow stationary androtating gears to coexist simultaneously. In a particular aspect, thecompound gear may include a partially-toothed drive gear that is gangedwith a partial disk that locks a concave surface ganged with thepartially-toothed driven gear to prevent rotation while othershafts/gears are rotating. In an exemplary embodiment, the driving shaftmay rotate 360 degrees per generally overlapping 90 degree rotations ofboth driven shafts, with the non-rotating shaft held fixed at eachdriving stage. Under these conditions the compound driven gears havetwice the effective diameter of the compound driving gears. Further,clutches and brakes may be used alternatively or additionally to thelocking mechanisms in the partially-toothed gears.

Still referring to FIG. 4A, in yet another embodiment, actuator assembly104, gearbox 400, the damper assembly 102, and/or the LFFC 100 ingeneral, is in operative communication with ancillary devices 164, suchas an electro-mechanical or pneumatic device. Merely by way of example,LFFC 100 system or components is in communicative operation with anotherair distribution device. Such devices may be fan-powered devices, airhandlers, chilled beams, VAV diffusers, unit ventilators, lights, fireor smoke dampers, control dampers, and pre-piped hydronics. Evenfurther, ancillary devices 164 may comprise other controls, sensors,firmware, software, algorithms, air moving devices, fluid movingdevices, motors, and variable frequency drives (“VFDs”). Still further,the LFFC 100 may be in communication or equipped with additionallinkages, gears or special actuators to turn additional concentrictubes, dampers, valves or rods to optimize air flow measurementperformance. The LFFC 100 may further be in combination with at leastone thermal transfer unit installed upstream of the device where theheat transfer surface may be much larger than the duct normal area,thereby allowing for at least one of a member selected from a groupconsisting of a lower air pressure drop, a lower water pressure drop, alocalized heating and cooling, a re-setting chiller, a re-settingboiler, and a reduced pump horsepower.

Still referring to FIG. 4A, in a different aspect, the LFFC 100 may befurther equipped or in communication with an ancillary device 164 thatis a built-in occupancy sensor, wherein the sensor is selected from agroup consisting of an infrared sensor, a motion sensor, an ultrasonicsensor, a temperature sensor, a humidity sensor, and a visual orinfrared camera. The built-in occupancy sensor may detect if a servicezone is occupied by persons, pets, activity, and the like, to adjust theflow of air thereto. For instance, if the zone is detected as vacant,the LFFC 100 may minimize, even shut off airflow to the room.

In still another embodiment, the actuator assembly 104 is furtherincorporated or in communication with a smart device 166 that may belocal or remote from the actuator assembly 104. The communication may bea wireless communication with a remote controller that operates theactuator assembly 104. In another aspect, the smart device 166 includesan algorithm for flow measuring, orifice metering and/or actuatormetering, and further controls the actuator assembly 104 depending onresults obtained by the algorithm(s). In still another aspect, it iscontemplated that the actuator assembly 104 outputs feedback, such asposition feedback, from at least one of the first and second actuators124,126 to a controller.

Referring to FIG. 4B, an embodiment of a rotary intermittent gearingarrangement 440 is generally shown. A driving gear 442 turning clockwiseis engaging driven gear 444 that turns counterclockwise locking drivengear 444. It can be seen that driven gear 444 is in a locked position asa convex portion 446 of driving gear 444 engages a concave portion 448of driven gear 444, including just the last point of contact with afinal driven gear tooth's 446 proximal involute. Drive gear 442incorporates a series of teeth 450 along 180 degrees of itscircumference and convex portion 446 on the remaining circumference ofdrive gear 442. Driven gear 444 incorporates teeth 452 along 90 degreesof its circumference and concave portion 448 adjacent teeth 452. Asshown in this embodiment, driven gear 444 rotates 90 degreescounterclockwise while drive gear 442 rotates 180 degrees clockwise.Drive gear 442 locks driven gear 444 for the remaining 180 degrees ofrotation. The rotational axis 454 of driven gear 444 may incorporate ashaft that operatively attaches and actuates either inner damper 112 orouter damper 108. A drive shaft 456 connect drive gear 442 to anactuator. Gear ratios may be modified to provides various rotation ratesand any desired degree of actuation overlap.

Turning now to FIGS. 5A-C, the LFFC 100 is shown mounted to a housing168. The housing 168 may be any shape, such as cylindrical as shown,tubular, rectangular, and so on. 1. In a particular aspect, the flowpathway is defined by a hollow inner surface 170 configured to removablyreceive the damper assembly 102 therein and an opposing outer surface172 configured to removably mount the actuator assembly 104 thereon.More particularly, the actuator assembly 104 and/or the stacking bracket128 is removably secured to a mounting bracket 174 that removablyengages the outer surface 172 of the housing 168. The mounting bracket174 may be configured to wrap around a portion of the housing 168. Inthis way, the mounting bracket 174 may be shaped to the geometric formand measurements of the housing 168.

As further shown in FIGS. 5A-C, the housing 168 may include mountingflanges 176 at an upstream end 178 and/or a downstream end 180. Themounting flanges 176 may have a plurality of holes 182 for receiving asecuring mechanism, e.g. screw, that further secures the housing 168 toa duct, such as a duct of an HVAC system. In that case, the fluid flowdownstream of the damper assembly 102 or orifice plate may be dischargeddirectly into an ambient space of a room. In another aspect, the housing168 includes a door or plate 184 as shown in FIG. 5B. The door 184covers an opening in the housing to permit permits access to the damperassembly 102 for maintenance, cleaning, and replacement of parts.

As shown in FIG. 5B, the inner surface 170 defining the flow pathwayduct through the housing 168 may include a gasket 186, such as aring-like compressible seal configured to compress and seal against theouter damper 108. Alternatively or additionally, the gasket 186 can beembedded on at least one of the outer and inner dampers 108,112, such asin a region where the inner and outer dampers overlap, or an outerperipheral edge of the outer damper 108.

In reference back to FIG. 1, the overlap region may include an outerperiphery 188 of the inner damper 112 and an edge of the outer damper108 defining the central opening 110. In yet another embodiment, thegasket 186 may be provided on an air valve stop, such as a metal ringabove an open damper area that provides a tight positive pressure sealwhen the damper is fully shut.

Turning now to FIGS. 6A-B, the housing 168 may form a venturi valve 194that defines a constriction section 196 for the flow pathway. The damperassembly 102 may be disposed in the constriction section 196. In oneembodiment, it is contemplated that a plurality of venturi valves ofdifferent sizes are ganged together in series upstream of the damperassembly 102 to simulate multiple variable venturi flow measurement. Instill another embodiment, it is contemplated that the housing is adouble-duct housing having two or more different sized inner and outerdampers to replicate a two-stage damper. In still another embodiment,the LFFC 100 is combined with 5 to 180 degree symmetrical elbowsdefining at least a portion of the flow pathway upstream or downstreamof the damper assembly 102, wherein the elbows or angled wallsprojecting into the flow pathway to adapt the device to tight spaceconstraints. For instance, the LFFC 100 may be installed withaerodynamically sound 45 or 90 degree elbows that can be oriented at anyangle to fit tight space constraints. It is contemplated that suchelbows are aerodynamically balanced to maintain proper airflow andoptimize the LFFC performance in confined space constraints.

Still, in other embodiments, the flow device may be housed in or incommunication with a wireless or hardwired variable air volume (“VAV”)diffuser, a grill diffuser, and/or a linear diffuser. In another aspectembodiment, the HVAC diffuser having the LFFC 100 or the LFFC 100 itselffurther comprises an all-inclusive light, such as a lighting deviceintegrated with and/or on the LFFC 100 to light a surrounding room orother environment. The all-inclusive light and/or an HVAC diffuser maybe controlled by one onboard controller, such as the LFFC controllerdescribed below. Merely by way of example, the all-inclusive light maybe one or more LED lights.

Referring back to FIG. 5C, a upstream sensor 254, such as an upstreamtap or Pitot tube may be placed in the flow stream. A downstream sensor250 may be placed in a flow wake or still air portion of the flowpathway, preferably within 1″ downstream of the concentric shafts. Inyet another embodiment, it is contemplated that a shaft of the damperassembly 102, such as the outer or inner shaft 114,116, provides orfunctions as an upstream and/or a downstream flow measuring device orsensor. In some embodiments, it is contemplated that the downstream orsecond sensor 250 senses a static pressure of the fluid flow. A totalpressure sensor could be used downstream, to the detriment of properfunctioning of the device.

Turning now to FIGS. 7A-D, the damper assembly 102 is shown disposed invarious housings or ducts with upstream and downstream sensors. In oneaspect, the housings or ducts may be existing housings or ducts and thedamper assembly 102, and/or LFFC 100, is retrofit installed into theexisting structures. FIGS. 7 A-C illustrate a circular, cylindrical duct252 with the two-stage damper assembly 102 disposed therein. The outerand inner shafts 114,116 may extend out of the duct 252 to an actuatorassembly 104 (not shown). The downstream sensor 250 is disposed at thedownstream end 180 of the cylindrical duct 252 adjacent to the shafts114,116. As mentioned previously, the shafts 114,116 may be attached tothe downstream sensor 250 and/or provide downstream pressure sensing. Insome aspects, the downstream sensor 250 is referred to as a secondsensor. A first or upstream sensor 254 is positioned in the flow pathwayat the upstream end 178. It is contemplated that the first and secondsensors 254,250 are used together to obtain the required pressuredifferential. The upstream sensor 254 may measure a total or, with someloss of sensitivity, a static pressure of the fluid flow. In someembodiments, it is contemplated that the second sensor 250 provides alittle sub-SP amplification. The sensor 254 may be a Pitot tube, orificering, or other pressure sensing device. 250 is a straightforward SP tap.

Still in reference to FIG. 7C, in yet another embodiment, an orificering 256 is installed upstream of the damper assembly 102 to impart anupstream stagnation circle from which total pressure may be tapped. Forthe circular duct 252, the orifice ring 256 may comprise 20 an orificeplate having an opening diameter that defines an area A_(op), wherebyA_(op)/A_(d) is approximately 0.8 or 0.9. In another aspect, the gasket186 may be installed on the cylindrical duct 252 and/or in the damperassembly 102. Still, in another aspect, it is contemplated that aplurality of damper assemblies, having the same or different stages, maybe installed in series upstream or downstream through the flow pathway.In that case, a pressure differential is determined between the upstreamand downstream sensors.

FIG. 7D illustrates a rectangular duct 258, whereby the damper assembly102 is shaped to fit the rectangular duct 258. More particularly, arectangular outer damper 108 r defines the central opening 110 thatreceives the inner damper 112. It is contemplated that the orifice platedefined by the damper assembly 102 increases a pressure of the fluidflow for the purpose of measuring and controlling fluid flow or massfluid volume. For instance, the orifice plate defines the variableopening 106. The variable opening 106 splits the fluid flow intomultiple streams for the purposes of increasing velocity pressure orrecovering velocity pressure for a more accurate measurement. Merely byway of example, a 10 inch round LFFC 100 can measure accurately down toabout 5 FPM. In a different aspect, the LFFC 100 is in operativecommunication with a duct or plenum that splits fluid flow into multiplestreams, such as a Y-shaped duct.

In yet another aspect, the LFFC 100 may be configured as a multipleoutlet plenum with two or more fluid device assemblies, wherein themultiple outlet plenum permits multiple accurate room or zone control ofmultiple rooms or zones simultaneously with at least member selectedfrom a group consisting of a single self-contained BTUH generatingdevice, a multiple thermal transfer device, an air to air HVAC system,and a fluid based system. Merely by way of example, the BTUH generatingdevice delivers heat energy to controlled rooms or zones. One BTUHdevice may be found in U.S. patent application Ser. No. 13/073,809 filedMar. 28, 2011 titled “MODULAR BUILDING UTILITIES SYSTEMS AND METHODS”,the contents of which is fully incorporated in its entirety herein.

LFFC Controller

Turning now to FIG. 8, the LFFC 100 may be in operative communicationwith a hardwired or wireless controller 300 that is local, onboard, orremote from the LFFC 100. The controller 300 comprises a processor 302and a memory 304 communicatively coupled with and readable by theprocessor 302 and having stored therein processor-readable instructionsthat, when executed by the processor 302, cause the processor 302 toperform one or more steps. It is contemplated that theprocessor-readable instructions are programmed for optimal performance,acoustics, and energy of the controller and the controlled damperassembly. In a different aspect, the processor-readable instructionscomprise an algorithm based on calculating fluid through orifices. Thealgorithm may be based on at least one of an orifice metering device, afluid sensing element, an actuator resolution, and a transducer.

In some embodiments, the controller 300 is a single microelectroniccontroller in communication with a plurality of room sensors 306 in aplurality of room zones to control the plurality of room zones. In someembodiments, it is contemplated that the controller 300 operates theLFFC 100 such that the HVAC system meets prevailing energy codes, suchas one or more of ASHRAE Standard 55-2010, ASHRAE Standard 62.1-2010,ASHRAE Standard 90.1-2010, ASHRAE Standard 62.2-2010, and ASHRAEStandard 90.1-2010.

For instance, the controller 300 may determine a pressure differentialbetween the first sensor 254 at the second sensor 250. Further, thecontroller 300 may determine a position of the outer and inner dampers108,112 based on a position feedback received from the actuator assembly104. Even further, the controller 300 regulates or controls the variableopening 106 based on the pressure differential and the position of theouter and inner dampers 108,112. In some embodiments, the controller 300determines a new position setting for the damper assembly 102, such as anew angle of rotation for the dampers, based on a flow rate. Thereafter,the controller 300 may signal the actuator assembly 104 to adjust thedamper assembly 102 to the new position. In other embodiments, thecontroller regulates the variable opening 106 based in part on aturndown ratio defined by a maximum volume of fluid flow through thevariable opening 106 to a minimum volume of controllable fluid flowthrough the variable opening 106, wherein the turndown ratio is a highturndown ratio that is greater than 10:1. More preferably, the turndownratio is greater than 100:1 or 250:1. With a high turndown ratio, theLFFC 100 may be self-commissioning.

In some aspects, self-commissioning allows for the LFFC to measure fluidflows within a system and set a damper position accurately, such as adamper extreme position, over any flow range required, without a needfor typical on site commissioning, for instance by a professionalbalancer. Further, it is contemplated that self-commissioning permitsthe LFFC to adjust any settings, such as minimum and maximum flows, onthe spot according to instructions sent from a network connection to theLFFC controller. For instance, an engineer may instruct the LFFCcontroller through their mobile phone to alter settings.

Still, in another embodiment, the controller 300 determines a flowcoefficient M_(F) based on a ratio of the variable opening area Ao to aflow pathway area, which may be a duct area A_(d). It is contemplatedthat the flow coefficient M_(F) discussed herein is therefore anon-constant variable and 0≤M_(F)≤1. The flow coefficient M_(F) may bebased on the position of the outer and inner dampers 108,112 and/ordetermined based on a calculation or a look-up table comprising aplurality of flow coefficients M_(F) that were previously determinedfrom testing, such as empirical data. In still another aspect, it iscontemplated that the controller 300 automatically calculates the flowcoefficient M_(F) based on the variable opening area A_(o). The flowcoefficient M_(F) calculation may be performed with a turndown ratio of10:1 or greater.

In a particular aspect, a table of measured flow coefficients versuspercentage open may be provided for each LFFC-based configuration andstored in the memory 304 of the controller 300. The table may be basedparticularly on the upstream sensor 254 being used. It is contemplatedthat if an actuator with significant hysteresis is mandated, no singletable can be used unless the hysteresis is uniform and predictable, sothat actual damper position can be calculated based on historical data,such as data collected from laboratory test. Alternatively, atheoretical formula for calculating the flow coefficient M_(F)coefficient provided and implemented by the controller. The theoreticalformula may include the Flow and Discharge Coefficient Correlations

$C_{F} = {\frac{A_{c}}{A_{o}} = \frac{c}{1 - {\left( {1 - c} \right)\left( \frac{A_{o}}{A_{d}} \right)^{2}}}}$for a flow coefficient M_(F) in combination with an upstream totalpressure sensor, or

$C_{d} = \frac{c}{\sqrt{1 - {\left( {1 - c} \right)^{2}\left( \frac{A_{o}}{A_{d}} \right)^{2}}}}$for flow coefficient M_(F) utilized in combination with an upstreamstatic pressure sensor.

In another aspect, the controller 300 may determine by calculation or alookup table the flow rate based on the pressure differential and theflow coefficient M_(F). The flow rate may be determined based onmultiplying the flow coefficient M_(F) with a square root of thedetermined pressure differential and then calibrated to read mass fluidflows in desirable engineering units. In a different aspect, thecontroller 300 determines a flow rate further based on a flowcoefficient that is applied at a maximum fluid flow to determine amaximum flow rate for use in calibration, further wherein the flowcoefficient includes a constant factor. The controller may furthercompare the flow rate to a target flow F or a desired temperaturesetting and/or operate the actuator assembly to maintain or change thevariable opening area A_(o) defined by the damper assembly 102 based onthe comparison. The target flow F may be one of a plurality of targetflow F's stored in the memory 304, or communicated to the controller 300based on input from a user or other wireless/hardwired system.

Still referring to FIG. 8, in yet another embodiment, the controller 300outputs at least one of the pressure differential, the variable openingarea Ao, the flow coefficient M_(F), and the flow rate to an externalcontroller or another controller 308. The controller 300 or 308 may be acloud-based control computing and wireless control components. Inanother aspect, the controller 300 is further monitored and controlledby BAS software of a BAS system, which may be represented as the othercontroller 308. For instance, the controller 300 balances the damperassembly 102 in real time from a front end software building automationsystem (BAS). Such real-time balancing data is displayed at a front endsoftware BAS system, a controller installed on self-containedcompressor, a fluid moving device, and a room air discharge device toallow the moving device to be controlled and interface with another 15equipment controller. In another aspect, the controller 300 providesreal-time turn down capabilities of a fluid moving device in operativecommunication with the damper assembly 102.

In reference again to FIG. 8, the controller 300 may output the flowrate to a central controller 310 at a central system that supplies thefluid flow to the flow device, LFFC 100. The controller 300 may furtheroutput the pressure differential to the central controller 310 tocontrol a variable frequency driver or inverter of the central system,such as an air flow movement device placed downstream or upstream of thedamper assembly 102. More particularly, the controller 300 may operate amotor of the air flow movement device based on the pressuredifferential. In some embodiments, the air flow movement devicecomprises one or more fans. In a further aspect, the controller 300 maycommunicate to the central system's central controller 310 that a limitof a control range has been reached, e.g., the damper assembly 102 iswide open, and/or the damper assembly 102 is out of the control range,e.g., the damper assembly 102 is wide open and unsatisfied.

Still referring to FIG. 8, the central controller 310 may be a centralcontrols system for use in an HVAC system. The central controller 310may comprise a central processor 312 and a central memory 314communicatively coupled with and readable by the central processor 312and having stored therein processor-readable instructions that, whenexecuted by the central 312 processor, cause the central processor 312to perform a plurality of steps. Merely by way of example, the centralcontroller 310 may receive and send data to and from a plurality of flowcontrollers generally indicated as 300 a-f. Each of the plurality offlow controllers 300 a-f may operate a flow device, such as an LFFC 100,positioned remotely from the central controller 310. The data receivedby the central controller 310 may comprise one or more of a pressuredifferential measured at each of the plurality of flow controllers 300a-f, a variable opening area of a flow pathway provided by each flowdevice, a flow coefficient M_(F) based on square of a ratio of thevariable opening area to a flow pathway area at each of the plurality offlow devices, wherein the flow coefficient M_(F) is a non-constantcoefficient and 0≥M_(F)≤1, and a flow rate based on the pressuredifferential and the flow coefficient M_(F).

Furthermore, the central controller 310 may send operational parametersto each of the plurality of flow controllers 300 a-f independently. Thecentral controller 310 may also adjust a volume of a supply fluid flowto at least a portion of the plurality of flow devices based on the datareceived. Further, it is contemplated that the central system mayoperate such that at all times, at least one LFFC 100 reports to it thata limit of the control range is reached; i.e. its damper is wide open;and no LFFC 100 reports that it cannot meet its target, generally flowrate or temperature. If an LFFC 100 reports that cannot meet its target,the central system may increase fan output if possible. If no LFFC 100is at a limit or out of the control range, the central system mayfeather back fluid flow supply. In a different aspect, if at startup,the central system operates with an LFFC 100 wide open and the pluralityof LFFC's 100 report operation out of the control range, then thecentral system may be preprogrammed to temporarily reset selected, lessessential delivery zones/rooms to receive a smaller portion of the totalsupply flow. For instance, preprogramming may include temporarilyresetting certain remote temperature set points. Such normal set pointsmay be gradually restored until all LFFC 100's report satisfaction;i.e., targets met, and at least one LFFC 100 reports operation at alimit of the control range; i.e., damper wide open. Normal set pointsmay be thus restored and supply flow may be controlled by the fans. In afurther aspect, the central controller 310 may be programmed to featherback rooms or zones that are not expected to be occupied and/or toprecondition certain rooms expected to be occupied.

Turning now to FIG. 9, a method 400 for controlling fluid flow through aduct defining a cross-sectional area A_(d) is shown. The method includesthe step of providing 402 a control element in the duct, whereby thecontrol element defines a variable opening area Ao that amplifies avelocity pressure of the fluid flow through the control element. Thecontrol element may refer to the damper assembly 102 described above. Insome embodiments, the control element is a thin blade control elementand the pressure differential ΔP is measured across the blade to enhancereadings. The method further includes measuring 404 a pressuredifferential ΔP across the control element, determining 406 a flowcoefficient M_(F) based on a ratio of A_(O)/A_(d), and determining 408 aflow rate Q based on a product of the flow coefficient M_(F), the ductarea A_(d), and a square root of the pressure differential ΔP. Further,the method may include comparing 410 the flow rate Q to a predeterminedtarget flow F to determine 412 if Q=F. If Q=F, the method includes thestep of maintaining 414 a setting of the control element defining thevariable opening area A_(O). If Q≠F, the method includes at least one ofthe steps of adjusting 416 the setting of the control element to a newsetting defining the variable opening area A_(O), notifying 418 acentral controller of a central system that supplies the fluid flow tothe control element to increase or reduce the fluid flow, and/oroperating 420 a speed of a fan disposed upstream or downstream of thecontrol element based on the pressure differential ΔP, damper % open,and/or satisfaction of temperature or ventilation requirements. In adifferent aspect, the central controller is a central zone or roomcontroller that adds fluid flow into and/or out of a controlled room orzone, and/or laboratory. In this way, two LFFC 100 devices (and/or theirrespective controllers) may be paired, providing an “in” device and an“out” device to provide a tracking pair for CFM tracking or, much moreeffectively, controlling room pressurization directly. In anotheraspect, a single controller may controller one or more LFFC 100 devices.

In another aspect, the method may include the steps of checking if thepredetermined target flow F has changed, and/or signaling an actuator toadjust the control element to the new setting. Still, the method mayinclude one or more steps of providing a plurality of control elementsin series or in parallel in the flow pathway, measuring the pressuredifferential ΔP across the plurality of control elements, anddetermining the flow coefficient MF based on the variable opening areaAo of the control element that is furthest downstream in the pluralityof control elements. In still another embodiment, the method includesthe step of enhancing or magnifying the measured pressure differentialΔP across the control element and calculating the flow rate Q based onthe enhanced or magnified pressure differential ΔP along with the flowcoefficient to achieve a precise flow rate Q.

Turning now to FIG. 10A, the LFFC 100 may be in operative communicationor constituted as a smart self-balancing air distribution (SBAD)adjustable diffuser 500. The diffuser 500 may have a temperature sensor502, such as a thermostat. The diffuser 500 may further comprise a motor504 operatively attached to a drive screw 506, that is furtheroperatively connected with a plaque diffuser body 508 and an adjustablediffuser 510. In particular, the adjustable diffuser may provide arecess 512 for receiving an end of the drive screw 506 therein. It iscontemplated that the diffuser 500 is inserted in a ductwork 514 tubing,such that the motor 504 and drive screw 506 are housed within theductwork 514. The plaque diffuser body 508 and the adjustable diffuser510 extend out of the ductwork 514 and may extend into a room. Inoperation, it is contemplated that the motor 504 moves the adjustablediffuser 510 toward and/or away from the plaque diffuser body 508 tocontrol an amount of airflow from the ductwork 514, 10 through theplaque diffuser body 508 and out around the adjustable diffuser 510. Forinstance, the motor 504 may be regulated by a sensed temperature of thetemperature sensor 502.

Turning now to FIG. 10B, a motorized SBAD diffuser variant 550 is shown.The diffuser 550 may be similar to the diffuser 500 except for thedifferences noted herein. In particular, the motorized diffuser 550comprises a plaque body 552, an adjustable diffuser 554, and anintermediary diffuser 556 disposed there between. The adjustablediffuser 554 and/or the intermediary diffuser 556 are adapted to movetoward or away from one another, and/or from the plaque body 552. Themovement may be effected by vertical movement of a drive screw 558 thatis connected to the diffuser components 552,554,556. In particular, amotor 560 having a toothed ring 562 may engaged corresponding teeth 555provided on the drive screw 558. In a particular aspect, theintermediary diffuser 556 provides an intermediary opening 564 that maybe sized corresponding to the geometric shape and size of the adjustablediffuser 554, such that the adjustable diffuser 554 may extend oroverlap with the opening 564. As shown in FIG. 10B, the plaque body 552,adjustable diffuser 554, and intermediary diffuser 556 are rectangular,although any shape and size, or combinations thereof, may becontemplated.

Turning now to FIG. 10C, a SBAD diffuser damper assembly 600 isillustrated. The diffuser damper assembly 600 may be similar to themotorized SBAD diffuser 550 and the diffuser 500 described above, exceptfor the differences noted herein. The diffuser damper assembly 600comprises a plaque body 602, an outer damper 604, and an inner damper606. In a particular aspect, the outer damper 604 is ring-shaped with adamper opening 608 defined centrally. The central opening 608 may becircular or otherwise and shaped corresponding to the geometric form ofthe inner damper 606, which is also circular as shown in FIG. 10C. Adrive shaft 610 is operatively connected with a motor 612 by a toothedcolumn 614 disposed along the drive shaft 610 that engages a toothedring 616 of the motor 612. In a particular aspect, the motor 612 rotatesto move the drive shaft 610 in a linear fashion, so that the outerdamper 604 and/or the inner damper 606 are moved toward or away from theplaque body 602.

FIG. 11 shows an example computer system or device 800, such as thecontroller 300, in accordance with the disclosure. An example of acomputer system or device includes an enterprise server, blade server,desktop computer, laptop computer, tablet computer, personal dataassistant, smartphone, and/or any other type of machine configured forperforming calculations. Any particular one of the previously-describedcomputing devices may be wholly or at least partially configured toexhibit features similar to the computer system 800, such as any of therespective elements of at least FIG. 8. In this manner, any of one ormore of the respective elements of at least FIG. 8 may be configured toperform and/or include instructions that, when executed, perform themethod of FIG. 9 and/or other instructions disclosed herein. Stillfurther, any of one or more of the respective elements of at least FIG.8 may be configured to perform and/or include instructions that, whenexecuted, instantiate and implement functionality of the controller 300,other controllers 308, and/or the central controller 310.

The computer device 800 is shown comprising hardware elements that maybe electrically coupled via a bus 802 (or may otherwise be incommunication, as appropriate). The hardware elements may include aprocessing unit with one or more processors 804, including withoutlimitation one or more general-purpose processors and/or one or morespecial-purpose processors (such as digital signal processing chips,graphics acceleration processors, and/or the like); one or more inputdevices 806, which may include without limitation a remote control, amouse, a keyboard, and/or the like; and one or more output devices 808,which may include without limitation a presentation device (e.g.,controller screen), a printer, and/or the like.

The computer system 800 may further include (and/or be in communicationwith) one or more non-transitory storage devices 810, which maycomprise, without limitation, local and/or network accessible storage,and/or may include, without limitation, a disk drive, a drive array, anoptical storage device, a solid-state storage device, such as a randomaccess memory, and/or a read-only memory, which may be programmable,flash-updateable, and/or the like. Such storage devices may beconfigured to implement any appropriate data stores, including withoutlimitation, various file systems, database structures, and/or the like.

The computer device 800 might also include a communications subsystem812, which may include without limitation a modem, a network card(wireless and/or wired), an infrared communication device, a wirelesscommunication device and/or a chipset such as a Bluetooth device, 802.11device, WiFi or LiFi device, WiMax device, cellular communicationfacilities such as GSM (Global System for Mobile Communications), W-CDMA(Wideband Code Division Multiple Access), LTE (Long Term Evolution),etc., and/or the like. The communications subsystem 812 may permit datato be exchanged with a network (such as the network described below, toname one example), other computer systems, controllers, and/or any otherdevices described herein. In many embodiments, the computer system 800will further comprise a working memory 814, which may include a randomaccess memory and/or a read-only memory device, as described above.

The computer device 800 also may comprise software elements, shown asbeing currently located within the working memory 814, including anoperating system 816, device drivers, executable libraries, and/or othercode, such as one or more application programs 818, which may comprisecomputer programs provided by various embodiments, and/or may bedesigned to implement methods, and/or configure systems, provided byother embodiments, as described herein. By way of example, one or moreprocedures described with respect to the method(s) discussed above,and/or system components might be implemented as code and/orinstructions executable by a computer (and/or a processor within acomputer); in an aspect, then, such code and/or instructions may be usedto configure and/or adapt a general purpose computer (or other device)to perform one or more operations in accordance with the describedmethods.

A set of these instructions and/or code might be stored on anon-transitory computer-readable storage medium, such as the storagedevice(s) 810 described above. In some cases, the storage medium mightbe incorporated within a computer system, such as computer system 800.In other embodiments, the storage medium might be separate from acomputer system (e.g., a removable medium, such as flash memory), and/orprovided in an installation package, such that the storage medium may beused to program, configure, and/or adapt a general purpose computer withthe instructions/code stored thereon. These instructions might take theform of executable code, which is executable by the computer device 800and/or might take the form of source and/or installable code, which,upon compilation and/or installation on the computer system 800 (e.g.,using any of a variety of generally available compilers, installationprograms, compression/decompression utilities, etc.), then takes theform of executable code.

It will be apparent that substantial variations may be made inaccordance with specific requirements. For example, customized hardwaremight also be used, and/or particular elements might be implemented inhardware, software (including portable software, such as applets, etc.),or both. Further, connection to other computing devices such as networkinput/output devices may be employed.

As mentioned above, in one aspect, some embodiments may employ acomputer system (such as the computer device 800) to perform methods inaccordance with various embodiments of the disclosure. According to aset of embodiments, some or all of the procedures of such methods areperformed by the computer system 800 in response to processor 804executing one or more sequences of one or more instructions (which mightbe incorporated into the operating system 816 and/or other code, such asan application program 818) contained in the working memory 814. Suchinstructions may be read into the working memory 814 from anothercomputer-readable medium, such as one or more of the storage device(s)810. Merely by way of example, execution of the sequences ofinstructions contained in the working memory 814 may cause theprocessor(s) 804 to perform one or more procedures of the methodsdescribed herein.

The terms “machine-readable medium” and “computer-readable medium,” asused herein, may refer to any non-transitory medium that participates inproviding data that causes a machine to operate in a specific fashion.In an embodiment implemented using the computer device 800, variouscomputer-readable media might be involved in providing instructions/codeto processor(s) 804 for execution and/or might be used to store and/orcarry such instructions/code. In many implementations, acomputer-readable medium is a physical and/or tangible storage medium.Such a medium may take the form of a non-volatile media or volatilemedia. Non-volatile media may include, for example, optical and/ormagnetic disks, such as the storage device(s) 810. Volatile media mayinclude, without limitation, dynamic memory, such as the working memory814.

Example forms of physical and/or tangible computer-readable media mayinclude a floppy disk, a flexible disk, hard disk, magnetic tape, or anyother magnetic medium, a compact disc, any other optical medium, ROM,RAM, and etc., any other memory chip or cartridge, or any other mediumfrom which a computer may read instructions and/or code. Various formsof computer-readable media may be involved in carrying one or moresequences of one or more instructions to the processor(s) 804 forexecution. By way of example, the instructions may initially be carriedon a magnetic disk and/or optical disc of a remote computer. A remotecomputer might load the instructions into its dynamic memory and sendthe instructions as signals over a transmission medium to be receivedand/or executed by the computer system 800.

The communications subsystem 812 (and/or components thereof) generallywill receive signals, and the bus 802 then might carry the signals(and/or the data, instructions, etc. carried by the signals) to theworking memory 814, from which the processor(s) 804 retrieves andexecutes the instructions. The instructions received by the workingmemory 814 may optionally be stored on a non-transitory storage device810 either before or after execution by the processor(s) 804.

It should further be understood that the components of computer device800 can be distributed across a network. For example, some processingmay be performed in one location using a first processor while otherprocessing may be performed by another processor remote from the firstprocessor. Other components of computer system 800 may be similarlydistributed. As such, computer device 800 may be interpreted as adistributed computing system that performs processing in multiplelocations. In some instances, computer system 800 may be interpreted asa single computing device, such as a distinct laptop, desktop computer,or the like, depending on the context.

Operational Algorithms

The LFFC described herein may be used in combination with a customalgorithm based on several mechanical construction features, such asconstruction, type of blade design, the material of the damperassembly/air valve (high end vs. low end version), and the like. Thisfeature may allow for cost effective production. The algorithm mayfurther depend on a type of actuator being used, based on resolution andapplication. In another aspect, the algorithm depends on a type of airflow sensing device being used, e.g., orifice ring, linear probe, crossflow sensor, electronic, etc. In still another aspect, the algorithm maydepend on the type of application, such as Chemical and BiologicalPharmaceutical, HVAC, Industrial Process Control and Equipment OEM.

In practice, it is contemplated that a cost effective first articlebuild of the air valve designed around performance parameters andchannel application is manufactured. The first article is then installedon a specially calibrated test stand/wind tunnel and tested/calibratedto the algorithm. Then, the algorithm is updated and the air valve istested again. Once characterized and tested, air valves are ordered andshipped to the field for Beta and cycle testing. The algorithm is thenscalable over the various sizes of the air valve commensurate to theactuator, air valve design and air flow sensor (above mentioned items).New actuator and flow instrumentation performance and accuracy can becalculated, rather than laboratory tested making introduction of newvariations faster. This feature may bring a new product to market muchmore rapidly than has been the case in the past.

Wind Tunnel Testing and Results

Three wind tunnel configurations were fabricated and employed. Industrystandards covering testing, like AMCA210.1999 Laboratory Methods forTesting Fans for Aerodynamic Performance Ratings do not adequatelyaddress the wide operating range. Finding a test setup that could test adevice with high range-ability was a challenge in and of itself. In onetest setup, the Wind Tunnel uses two different inlets (Hi & Lo) to coverthe performance range of the LFFC since a single fixed setup could notdesigned to cover the range. Existing micro-manometer air pressuringsensing technology also makes accuracy testing over a broad operatingrange difficult. Furthermore, special software programs had to bewritten for the base software program, the sophisticated lab typecontrollers, and the highly accurate and calibrated sensors forverification purposes. Unlike other air flow tests, this test includedthe resolution points from the electronics such as actuators at thevarious performance parameters, the type of fluid sensing element beingused, the construction of the device, the various fluid patterns atvarious performance spectrums and the type of transducer commensurate tothe algorithm. All this data collected at thousands of points ofperformance parameters, as we mirrored real time operation of an actualbuilding system. Therefore, the test stand/wind tunnel was complex andvalidated the LFFC described herein. Moreover, the test stand/procedureexecuted and reduced the R&D time by several years.

A ratio test on a 10″ low flow damper/flow meter was undertaken. Inparticular, the study utilized a 2-stage damper calibrated to functionas a flow station. At any fixed damper position the device serves as anorifice plate, with flow coefficient¹ which may be considered a fixednumber over a wide range of Reynolds numbers. Each damper position hasan associated critical Reynolds number below which the coefficient canbe regarded as Reynolds-dependent. ¹C=(duct VP/DeviceDP)^(0.5)

Test results showed that with the instrumentation at hand, no Reynoldsdependence was noted over the entire range of annulus positions (disk100% open). The flow coefficient may be regarded as constant at eachannulus setting; i.e., a function of damper position only. With annulusclosed, a possible critical Reynolds number was determined at diskopenings 40% and 80%.

Low Flow Air Valve 3 inch Ratio Test

A disk at 40% open ratio was tested and yielded a chart that plots C²,the ratio of the Setra reading on the disk, to the MKS 3″ Venturireading at disk 40% open. The ratio remains substantially constant untilthe lowest two points are reached. At the lowest point, C² reads ˜10%high, so C ˜5% high. Velocity 31 FPM (6109 MPS), 17 CFM (481 LPM) in the10″ (25.4 CM) duct (note that this is about 1/10 walking speed).Turndown ratio 97 with respect to a full 15 flow duct velocity of 3000FPM (590 kMPS) and still 39 with respect to 1200 FPM (236 kMPS), stillan excellent turndown relative to the low fluid flow velocity, which isuncontrollable in existing systems. Venturi Reynolds number ˜9000, stillin the flat flow profile range. Reynolds number 2600 in the Duct, sovelocity profile moving toward parabolic, which would increase theDamper delta P, possibly slightly offset by a decrease in orifice ringamplification, but not so abruptly as in the curve.

A disk at 80% open ratio was tested and yielded a chart that plots C² atdisk 80% open. The ratio remains substantially constant until the lowestpoint is reached. At that lowest point, C² reads ˜10% low, so C ˜5% low.Velocity 44 FPM (8663 MPS), 24 CFM (670 LPM) in the 10″ (25.4 CM) duct(note that this is about 1/10 walking speed). Turndown ratio 68 withrespect 25 to FPM full flow duct velocity of 3000 FPM (590.7 KMPS), 27with respect to a still controllable 1200 fpm (236.2 KMPS) full flow.Venturi Reynolds number ˜12000, well into the flat range. Reynoldsnumber 3800 in the Duct, so velocity profile moving a little towardparabolic, which would increase the Damper delta P, possibly slightlyoffset by a decrease in orifice ring amplification, but the displayedratio drops abruptly in the curve. In the wrong direction to be aReynolds effect. Therefore, look at sensor and transducer limitations.C=(duct VP/DeviceDP)^(0.5)

Calibration of the 1″ (249 Pa) Setra yields a chart that plots the ratioof readings of the 1″ (249 Pa) Setra used in these tests to the MKSstandard. The Setra tracks well down to 0.02″ w.g (4.98 Pa). It reads 8%high at 0.01″ (2.49 Pa), corresponding to 4% in flow coefficients. TheSetra remained above 0.02″ (49.8 Pa) in these tests which is not theproblem. May need to calibrate sensors against each other at these lowflows.

This data will be refined using a 0.1″ (24.9 Pa) delta pressure MKStransducer (on order), encompassing more disk settings than the 40% and80% considered here, and extending 10 to even lower flows. In theprocess the current contradiction between 40% and 80% low end behaviorwill be resolved.

Flow Coefficient Data and Curves

In this series, 2—1 minute averages were taken over each 2 minute longdamper setting, labeled Early and Late or 1st pt, 2nd pt. It may nothave been possible to align sampling with repositioning, so Earlyaverage may include data from previous setting and repositioninginterval.

Low Flow Air Valve 3 inch Char Test JCI

The 1″ (249 Pa), 2″ (498 Pa) and 10″ (2490 Pa) Setra tracked each otherquite well up to 60%, where the 1″ Setra maxed out. The 2″ (498 Pa)Setra maxed out at 65%, and the 10″ 20 (2490 Pa) Setra at 90% opening,85% closing. The artificial hysteresis caused by sensor saturation at90-100% open is evident in the graph. Saturation lowered those plottedvalues, particularly at 100% Open. Similar artifacts are evident in theconsiderably lowered 1″ (249 Pa) and 2″ (249 Pa) Setra saturationcurves. The JCI actuator introduced no significant hysteresis: openingand closing data were often identical to 4 decimal places, occasionallydiffered by a few 25 percent. Early readings were not noticeablycontaminated by vestiges of the previous setting.

Low Flow Air Valve 3 inch Char Test GAP Actuator

The late (2nd minute) data shows the 1″ (249 Pa), 2″ (498 Pa) and 10″(2490 Pa) Setra again tracked each other quite well up to 60%. Abovethat, and over the entire early (1st minute) range, very considerablehysteresis is apparent. Since 2nd minute data is greatly improved over30 1st minute data, we may try testing at 3 minutes; 3 readings persetting: a long relaxation time may be involved. In 2 minutes at the100% setting the damper had not achieved 100% opening 41 from indicated95%. The 100% early reading is higher than the later reading. The 90 and95% early readings reduce to about the late 100% reading, but the late95% reading is the highest of the whole set, giving the appearance thatthe actuator oscillates back and forth several times when commanded toreverse direction, before settling into (in this case) closing mode,lagging 5 about 9 degrees behind the opening path early, reducing toabout 2 degrees after 2 minutes in position. Satisfactory agreement maybe achieved 3 or 4 minutes after a position-changing command.

Benefits of the LFFC in HVAC systems

The LFFC described herein may be incorporated in an HVAC system tofacilitate the HVAC system in providing comfort at low-as-possibleenergy consumption levels. The American Society of Heating,Refrigerating and Air-Conditioning Engineers (“ASHRAE”) establishedstandards outlining room conditions that are acceptable for most, i.e.80%, of building occupants. In particular, the ASHRAE provides apsychometric chart that shows comfort zones as defined in ASHRAE Std. 55for summer and winter seasons. The ASHRAE Std. 55 identifies the comfortzone or range of conditions that satisfy most people who areappropriately dressed and performing light work, e.g. office work.People wearing heavier clothing and undertaking heavy work may needcooler conditions. Comfort in a controlled space depends on acombination of air flow temperature control and humidity.

Further, comfort is interrelated with ventilation of fresh air.Supplying metered amounts of outside air prevents the indoor air frombecoming stale and unhealthful. The LFFC described herein measures andmeters fluids, such as air or fresh air, into controlled zones toprovide comfort to people in those rooms. It is noted that outdoor airstandards have become more strict and created a demand for a higherturndown air controlling device. With the high turndown LFFC describedherein, the LFFC can be incorporated into the HVAC system to promoteconditioning of supply air and help provide each space or zone a portionof the conditioned fresh air within a comfort zone that has acceptablecombinations of humidity and temperature.

Further, as defined in ASHRAE Std. 62 Fresh Air Standard, the HVACsystem should provide sufficient amounts of outside air for humancomfort ventilation. The effectiveness of the system to accomplish thisdepends on two main factors: 1) Quantity of supply air, which may bemeasured in cubic feet per minute (“CFM”) or liters per minute (“LPM”)and 2) temperature of the supply air, which may be measured in degreesFahrenheit or Centigrade. To heat or cool a space, the quantity andtemperature factors are combined in different ways depending upon thetype and design of the particular HVAC system. A thermodynamic equationthat incorporates these factors is shown below for sensible heating andcooling where humidity is not included. In the equation below, theconstant (“Constant”) and mass flow (“CFM”) may be adjusted for liquidfluid flows.

$\begin{matrix}{{BTU}\mspace{14mu}{Equation}\mspace{14mu}{Relating}\mspace{14mu}{Flow}\mspace{14mu}{and}\mspace{14mu}{Temperature}\mspace{14mu}{to}\mspace{14mu}{Energy}\mspace{14mu}{Transfer}} & \; \\{{BTU} = \left( {{Constant} \times {CFM} \times {Difference}\mspace{14mu}{in}\mspace{14mu}{Temperature}} \right)} & {{Equation}\mspace{14mu} 1}\end{matrix}$

The above equation shows that BTUs delivered to condition a space areaffected by 10 the amount of air and/or air temperature. Changing eithervariable, the mass flow CFM (LPM) or temperature ° F. (° C.), can changethe temperature in a controlled zone. In a particular aspect, the LFFCdescribed herein measures and meters the mass flow CFM and gallons perminute (“GPM”) flows, and other variables, into controlled spaces.

Commercial offices need to utilize ventilation systems that provideindoor climate conditions that comply with fresh air and energy codes.The airflow may be independent of room occupancies, and therefore,existing ventilation systems may waste energy in unnecessarily supplyingfresh conditioned air to unoccupied zones, e.g., zones without people.Wasted energy generates unnecessary utility costs. In order to complywith new energy standards, HVAC systems should reduce air flow whenpeople are not present. The LFFC described herein may facilitate theadjustment of air flow so the necessary ventilation is provided, whilenot sacrificing temperature quality and C02 concentrations. Inparticular, by providing cool conditioned air at 55° F. (13° C.)simultaneous cooling, heating and humidity control are possible. Thecool 55° F. (13° C.) air can remove the excess heat and humiditygenerated by people, plug loads, computers and incoming sunlight. Inother cases, zones within buildings may require both heating, coolingand humidity control all in a short time period, e.g. a single day. Inthat case, the HVAC system can be capable of reheating air, which isheating air that was previously cooled to 55° F. (13° C.). The LFFCdescribed herein can measure smaller air and fluid volumes with highturndown. Further, the LFFC described herein offers precise fluid flowmeasurement that also generates lower sound levels, while providingfresh air to zone occupants and reducing energy consumption, inparticular by reducing the need for reheat.

LFFC controller technology enables installation of systems with noreheat boxes. For morning warmup, an inexpensive unit heater located inthe MER outside air/return air mixing area replaces the reheat boxes andthe attendant building-wide piping or heavy wiring. In reheat mode, theLFFC reverses thermometer control loop operation, becoming satisfiedwhen the zone temperature reaches a centrally provided warm-up setpoint. It also may control nearby peripheral heating units. The centralsystem reverts to normal operation when the number of LFFC controllerscalling for cooling exceeds the number still calling for heating, whichwill generally be on the Northernmost face of the building. Peripheralheating is generally operative near the windows, so these zones continueto be heated as needed. If some zones still require heating aftercooling is 90% satisfied, the central controller may alternate episodesof cooling and heating until there are no more calls for heating. Thisis made possible by timely communication between the central controllerand the LFFC's, and the ability of the FFFC to feather subject to MOArequirements maintained using local CO₂ sensors or preset rules ofthumb. When this cannot be accomplished without overcooling/heating theLFFC advises the central controller to increase % outside air (which mayhave been set at zero at the beginning of the morning warmup cycle. Theabove arrangement is vastly more efficient than cooling central air to55 F followed by reheating to 90 F at the periphery.

In another aspect, humidity increases and decreases along with indoorair temperature variation. The LFFC described herein may facilitate theHVAC system in maintaining indoor humidity within the comfort zone. Forinstance, an HVAC system in a dry climate may include an addedhumidifier unit in the central air handler to increase the moisturelevel in the conditioned air when required. An HVAC system in a humidclimate may dry or remove moisture from the supply air by overcoolingthe conditioned air and then reheating it back to the comfort zonetemperature. The LFFC described herein makes these processes moreefficient by more accurately measuring and controlling air and fluidquantities.

In a further aspect, the LFFC described herein can be used in bothcentral HVAC and zone HVAC systems, including air to air andwater/fluid-based systems. Central HVAC systems may include largeheating and cooling equipment that condition massive amounts of air forlarge areas on multiple floors of buildings. Such equipment may belocated in basements and/or on roofs of the buildings and include, forexample, steam boilers, hot water heaters, chillers, cooling towers andbackup generators. Zone HVAC Systems may comprise smaller pieces ofheating and cooling equipment. Such equipment may be placed withinbuildings to control zone or room level spaces. Zone control systems maycontrol individual occupied spaces and represent a majority of coolingand heating equipment installed in the building.

Due to the advent of efficient low horsepower ECM's, it is now possibleto hang efficient small AHU's in the ceiling space so HVAC takes away nofloor space. Elimination of supply and return shafts saves more spacethan is lost to compact local units. Elimination of the return stacksimultaneously eliminates stack effect and the need for return fans, soit is not difficult to design much more efficient 2500 CFM ceiling unitsthan is achievable with central MER's. With care, HW and CW can be runto the units through the same pipes connecting via solenoids to the HWand CW risers. It is contemplated that the LFFC described herein can beimplemented in both of the central and zone systems, with and withoutfirmware and software.

It is worthy to note that an HVAC system for a building can provide avariety of different heating and cooling zones, particularly for a largebuilding having numerous spaces.

Different zones within a building have different heating and coolingneeds, which may depend on thermal heat gains, geographic locations,number of floors, numbers and sizes of windows and doors. For instance,large buildings with inner cores insulated from the outdoors may notrequire heating during the winter months, but may require coolinginstead. On the other hand, outer zones or perimeter spaces along theouter walls may require heating due to cold air convection andelectromagnetic (“EM”) radiation passing through the windows. Further,all zones, whether heating or cooling, require fresh air ventilation. Itis contemplated that the LFFC described herein aids the HVAC system tomeet both new fresh air standards and energy standards at the same time,while providing the variety of heating and cooling zones. TheLFFC-incorporated HVAC system is capable of adjusting air flow withoutcausing significant pressure differences that may lead to considerableamounts of turbulence, i.e. sound that is distracting to buildingoccupants. More importantly, LFFC's work fine at 1500 FPM or even 1200FPM maximum compared to 3000 FPM or more for legacy VAV boxes,eliminating the principal source of HVAC noise problems in occupiedspace and reducing fan TP by more than the 1 in. wc. required by VAVboxes. LFFC's operate with 0.02″ pressure loss, enabling the ceilingunits mentioned above to operate at less than 1″ TP: at least 5 or 6times as efficient as the best legacy central systems with return orexhaust fans.

Application of the LFFC in VAV systems

One type of HVAC system is a variable air volume (“VAV”) system. It iscontemplated that the LFFC described herein can be incorporated in VAVsystems. In particular, the VAV system may include one or more supplyducts that distribute supply air at 55 of (13° C.). The supply airtemperature in the VAV system may be held constant. The air flow rate inthe VAV system may be varied to meet varying heat gains or losses withinthe thermal zone served. The VAV system may further include VAV fancapacity control through electronic variable speed drives orelectronically communicated motor (“ECM”)/solid state motor technology.Such VAV fan capacity control may greatly reduce the energy consumed byfans and thus a substantial part of the total energy requirements of thebuilding served. The capacity controlling supply and return fansmodulate the air volume up and down depending on thermal loads. Further,the VAV system may provide dehumidification control in a cooling mode,whereby supply air volume is reduced and reheat is introduced fordehumidifying. This can be done efficiently using a heat pipe. In largercommercial systems, the VAV system may include one or more VAV airhandlers to serve multiple thermal zones such that the air flow rate toeach zone may be varied. In that case, the VAV system may utilize theLFFC described herein, which may replace or be used in additional totraditional VAV terminal boxes.

The various LFFC devices described herein eliminate VAV terminal boxesas a primary zone-level temperature flow control device. The LFFC is acalibrated air damper equipped with an automatic actuator and air flowsensor. The LFFC is connected to a local or a central HVAC system. InVAV systems, fan capacity control is critical, since ever-changing ductpressures can influence the amount of air (CFM) delivered to zones.Without proper and rapid flow rate control, the VAV system can delivertoo much air or generate excessive noise and potentially damage ductworkby over-pressurization.

In VAV cooling mode, the LFFC decrements to limit flow of cool air intospaces where zone temperatures are satisfied. When the zone temperatureincreases again, the LFFC increments to introduce larger volumes offixed temperature air in order to cool the zone space temperature. Inthe VAV system, a central fan may maintain a variable supply of air.Unlike legacy VAV terminal boxes, which operate independently of eachother, LFFC's are in constant communication with each other and withcentral control as they supply conditioned air throughout the buildingzones. As Legacy VAV terminal boxes close, duct static pressureincreases and the control system slows the fan down to restrict thevolume of air going through the VAV system, and as the VAV terminalboxes open, the fan speeds up and allows more air flow into the ductsystem. The tight communication between LFFC's and central controlenables exactly satisfying all LFFC's with no excess pressurization andno minimum pressure maintained anywhere in the system. With no minimumpressure set, fans can be selected in their maximum efficiency range atdesign flow without incurring danger of fan stall at lower flows. Bycontrast, in legacy systems, centralized building controllers stillmeasure and wastefully maintain constant static pressure in the supplyducts. In addition to being wasteful such practice biases the systemcurve in the direction of fan stall. The LFFC needs 0.02″ minimum andeven that need not be maintained artificially; it is satisfied naturallyin the simple central—peripheral interchange protocol outlined above.

Obviously, the LFFC may be placed in a ceiling or underfloor ductwork.The LFFC controls the volume of the air to the zone to maintain targettemperature. In some cases, each zone has a thermostat that controls theLFFC by indicating when to modulate the air damper based upon the zoneheating or cooling demand. For instance, a controller in the LFFC maytake the thermostat's measured room temperature as an input, incrementor decrement the LFFC damper proportional to the temperature deficit,and repeating at intervals to adjust the damper as necessary. In thisway, the LFFC delivers fixed supply air temperature at required varyingvolume rates.

When sizing Legacy VAV terminal boxes, a substantial number of sizeswere required for accurate flow measurement commensurate with acousticalrequirements. The wide LFFC rangeability eliminates this need: a fewsizes suffice for the entire range of design CFM's. To maintain flowmeasurability and control, an inlet of a legacy VAV terminal boxrequires high pressure/high velocity entering air, which is dissipatedwithin the casing of the device to provide required low velocity/lowpressure output air, with generation of considerable low frequencynoise. LFFC's have essentially no minimum pressure requirement andoperate over a range of much lower velocities entailing greatly reducednoise production. The inlet is connected to a system of supply ductsthat is in communication with the Central Air Handling Unit. An outletis in communication with an outlet duct leading to one or more zonediffusers. The LFFC may open or close to control the amount ofconditioned air flow needed. The air damper may be controlledautomatically by a motor, also referred to as an actuator, which iscontrolled by the controller based on inputs from the thermostat and airvolume sensors. The thermal sensor may be placed in the zone to detecttemperature and instruct the damper of the LFFC to open or closeincrementally. This controls the amount of fixed temperature conditionedair into the zone. A few LFFC sizes replace typically 21 differentlysized legacy VAV terminal boxes along with various size coils inmanufacture.

In a legacy assembly, the VAV terminal box along with the air flowsensors might be supplied by sheet metal manufacturers. Controlscompanies might install the direct digital VAV controller (“DDC”) withactuator and transducer after the fact, connecting into the air flowsensor and operating the damper shaft. Testing of VAV terminal boxesmight include noise and leakage rates. In some cases, the legacy VAVterminal box is oversized or installed in uncontrollable spaces orzones, thereby generating control problems that result in reduced indoorair comfort, increased energy costs, zone controllability problems andmaintenance problems. The ASHRAE RP 1353 standard validates the poorperformance of VAV terminal boxes with DDC controls at low flow. LFFCmanufacturers provide single source pre-commissioned wide control rangedevices that virtually eliminate the difficulties just described.

Traditional VAV terminal boxes in VAV systems have turndown ratios under5 to 1 from 3000 FPM, despite promotional claims to the contrary.Traditional laboratory control air terminals have slightly higherturndown ratios of up to 10-1. It is contemplated that the LFFCdescribed herein may be incorporated into the VAV system described aboveand offer higher turndown ratios that are greater than 10-1, or greaterthan 100-1, or greater than 250-1. Turndown is important for a varietyof reasons, including the following: 1) Accurate measurement of the airand water (glycol and water used interchangeably) volumes beingsupplied, particularly important in laboratories where infectiousdiseases and toxic chemicals are present. 2) fewer part numbers, i.e.fewer devices are required to cover operating ranges. This allows forfundamentally simpler designs and systems, including streamlining and/orcombining product portfolios and reduced manufacturing costs. 3) Lowerpressure drops providing quieter air/fluid delivery systems and lowerenergy costs and superior acoustics. 4) Reduced Life Cycle costs of thebuilding and cost of ownership. 5) Lower installed and first cost due tofundamentally fewer components and simpler equipment sizing. 6)Streamlined controls system architecture and software hosted in thecloud or through enterprise/legacy system. It is contemplated that theLFFC described herein provides a minimum turn down ratio of over 100-1with respect to legacy device velocities, at a much more desirableenergetically and acoustically FPM, depending on the design withmultiple orifices, dampers and/or valves. This lends to fewer partnumbers, lower manufacturing costs, lower system installed costs,smaller footprints, reduced cost of ownership and lifecycle, morestandardized HVAC duct designs, quieter systems and less energy used tomove fluids to the occupied zones.

Application of the LFFC in Dampers

In another embodiment, it is contemplated that the LFFC described hereinprovides an air flow damper assembly that can be used in conjunctionwith VAV or other HVAC systems. In particular, the damper assembly canbe formed in many geometries and shapes, and used additionally oralternatively with existing damper devices, which may often becustom-ordered due to special size and configuration constraints. Thedamper assembly of the LFFC disclosed herein can be used in a variety ofapplications, including in emergency fire and smoke situations. Inparticular, the damper assembly of the LFFC may be utilized for turningair on and off and modulating in between the two extremes. The damperassembly disclosed herein may also be used in or with fan coils and unitventilators that heat and cool spaces. Such unit ventilators may besimilar to fan coils, but also introduce outside air into theventilation system. Merely by way of example, unit ventilators may belarger with higher BTU capacities. Therefore, the high controllabilityof the damper assembly and/or LFFC disclosed herein may offersignificant improvements in the efficiency of such systems.

In another aspect, it is contemplated that the damper assembly and/orLFFC disclosed herein can be used in laboratory spaces for fire andcontamination control purposes, such as in fume hoods where chemicalreactions take place. The damper assembly disclosed herein may alsoregulate the fresh air into hospital rooms.

In another aspect, the LFFC disclosed herein may provide a damperassembly for use in Central Building Air Handlers (“AHUs”) to controlair supply into the building, exhaust air out of the building, and mixthe two air streams to conserve energy. The damper assembly disclosedherein may replace or be used in conjunction with an existing damper inthe AHU to simplify control of the damping mechanism. Large parallelblade LFFC's described herein handle the large air volumes typical ofAHU's. The damper assembly disclosed herein may be used in ductwork andin air distribution devices which deliver air into the zone. Further,the damper assembly may be used in refineries and process applications,including industrial applications and air pollution equipment. Stillfurther, it is contemplated that the damper assembly can be used inconjunction with thermal transfer devices, e.g. facilitate design ofmore efficient thermal transfer units, which may reduce energy, product,and installation costs. In another aspect, the damper assembly describedherein may be controlled by controllers and tied into networks. In thatcase, the amount of equipment required and the amount of control pointsmay be reduced, yielding more cost efficient control networks withsophisticated capabilities that can be integrated in buildings andcontrolled/monitored through cloud computing and centralized 30locations. In this way, the damper assembly and/or LFFC disclosed hereinmay utilize open source controls, as opposed to proprietary legacysystems.

Implementation and Operation of LFFC in HVAC Systems

It is contemplated that the LFFC described herein controls temperatureand air flow for an HVAC system by utilizing air flow measurements andthe damper configuration described herein, which allow for more preciseair measurement and regulation. The LFFC may be retrofit into existingHVAC systems, replace and/or be used in conjunction with existing VAVterminal boxes, and/or be incorporated in new HVAC system designs.

In one aspect, the LFFC utilizes lower pressure models for controllerdelta-pressure (ΔP) transducers. In this way, air pressure measurementenables or makes possible pressure independent control. Transducers arethe most costly electronic element in typical HVAC VAV controllers.Furthermore, the LFFC can be used with more expensive pressure, siliconand electronic transducers for even greater control, but works fine withvery inexpensive transducers.

Control Algorithms—Pressure Independent PI Control of Temperature

The LFFC described herein gives inherently pressure independent controlof airflow, wherein the control of the airflow is independent of inletair pressure conditions. For instance, when several LFFC devices are onthe same supply air duct branch and each is opening and closing tocontrol local zone temperature, they impact the air pressure down thesupply duct. The inherently pressure independent LFFCs Maintain flow ortemperature target values independent of pressurization while workingwith the central fan controller to maintain the least pressureconsistent with satisfying all LFFC's. This is done very simply: fanpressurization is constrained so that at least one LFFC is wide open atall times, and no overpressurization. This was not possible with legacysystems.

The LFFC may further be used with a Pitot sensor for sampling airpressures in the conditioned air stream that is further piped to the airflow transducer on the DDC controller. In one embodiment, a dead endtransducer is used, i.e. air does not flow through the transducer, whichmay prevent clogged sensors, hoses, and transducers since aircontaminants are not trapped therein. Such transducers may beimplemented in hospital ventilation systems, since air in hospitals tendto be filled with lint, which clogs transducers. It is contemplated thatthe LFFC requires little or no maintenance, due at least in part toreliable air flow measuring for an extended period of time.

Air Velocity Measuring, CFM, Flow Coefficient and Calculations

Air in a duct has two components to be measured. A first sensortypically senses flow Total Pressure by creating a stagnation zone whereair impinges directly on the face of the sensor. It is noted that theterm “transducer” used herein will refer to a device that measures airpressure and converts to electrical signals that is located on or nearthe electronic DDC controller. The flow pickup or sensor samples theflowing air and sends to the transducer. A second sensor out of thedirect airstream senses static pressure, which pushes in every directionwith the same force with or without air flow.

Air velocity is measured in feet per minute using the two aircomponents, total pressure and static pressure, each measured separatelyand subtracted from one another to obtain velocity pressure, inaccordance with Bernoulli's Principle. This pressure difference isreferred to as delta pressure and it is abbreviated as ΔP. Themathematics of this measurement is as follows:

$\begin{matrix}{\mspace{79mu}{{Total}\mspace{14mu}{Pressure}\mspace{14mu}{Equation}}} & \; \\{{\Delta\; P} = {{{Total}\mspace{14mu}{Pressure}\text{-}{Static}\mspace{14mu}{Pressure}} = {{Velocity}\mspace{14mu}{Pressure}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Air velocity in feet per minute, abbreviated as FPM, is calculatedrelative to DP in inches H20 and fluid density in lb./ft3 using thefollowing equation:

$\begin{matrix}{\mspace{79mu}{{Air}\mspace{14mu}{Velocity}\mspace{14mu}{Equation}}} & \; \\{{{Air}\mspace{14mu}{Velocity}\mspace{14mu}{in}\mspace{14mu}{FPM}} = {{1097*\left. \sqrt{}\left( {\Delta\;{P/{density}}} \right) \right.} \sim {4004*\left. \sqrt{}\Delta \right.\; P}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

Readings of electronic pressure transducers in common use are highlydependent on ambient temperature. In high precision applications,“Auto-zeroing” greatly reduces this effect. Auto-zeroing involvesconnecting the transducer inputs together so that the transducer voltagedrift at zero pressure difference can be measured and used to compensatereadings with restoration of the transducer sensor connections. Thesensor used herein may provide total pressure in the “High” pressuretube and the static pressure in the “Low” pressure tube. The subtractionis accomplished at the controller transducer by putting total pressureon one side of a diaphragm and static pressure on the opposite side.This provides a mechanical subtraction of the two separate pressures.

Air velocity pressure is commonly measured in inches of water column.For reference purposes, there are 27.7 inches of water column in one PSI(6.89 kPa).

Air Volume Calculations

$\begin{matrix}{\mspace{79mu}{{Total}\mspace{14mu}{Volume}\mspace{14mu}{CFM}\mspace{14mu}{Formula}}} & \; \\{{CFM} = {{FPM} \times {Duct}\mspace{14mu}{Area}\mspace{14mu}{in}\mspace{14mu}{square}\mspace{14mu}{feet}\mspace{14mu}\left( {{as}\mspace{14mu}{measured}\mspace{14mu}{at}\mspace{14mu}{LFFC}\mspace{14mu}{inlet}} \right)}} & {{Equation}\mspace{14mu} 4} \\{\mspace{79mu}{{Duct}\mspace{14mu}{Area}\mspace{14mu}{Calculation}}} & \; \\{{{Duct}\mspace{14mu}{Area}\mspace{14mu}\left( {{round}\mspace{14mu}{duct}} \right)} = {n \times \left( {{duct}\mspace{14mu}{diameter}\mspace{14mu}{in}\mspace{14mu}{feet}\text{/}2} \right)^{2}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Airflow in CFM (cubic feet per minute) is calculated from FPM (feet perminute) and multiplied by the LFFC inlet duct area or the opening areawhich the flow pickup sensor is located within. Airflow or velocitypressure (“VP”) is the difference in the total pressure (Tp) and staticpressure (Sp), or high and low. A cone in front of the Sp portartificially decreases the Sp relative to the Tp, thereby makingreadings higher and more sensitive at low flows where pressuredifferences may become as low as 0.008 inches of water (1.992 Pa). Thecone forms an obstruction that raises local velocity in the stagnantzone surrounded by the wake, thereby lowering the static pressure at theSp tap located therein and making the pressure differential readingshigher. Amplification at low flows is highly desirable, where the VPbecomes too small to be measured with a typical inexpensive pressuretransducer. Since the reading is no longer representative of the actualflow, the amplification can be removed from the ultimate reading toarrive at an accurate air flow calculation. This may be performed bymodifying the flow coefficient and/or flow coefficient.

A flow pickup may artificially depress Sp at the downstream tap toimprove flow pickup sensitivity. To get a calibrated, accurate CFM (LPM)reading, this enhancement can be mathematically removed from CFM (LPM)readings. Further, duct inlet conditions in field locations varydramatically and can negatively impact pickup sensor accuracy. To obtaina good reading, there may be three to five straight duct diameters ofstraight duct piping in front of the pickup. In some cases, this may beprohibited due to construction constraints. Flexible duct may be used tomake short length connections between straight round duct other inlets.The flex duct imparts a circular swirl to incoming air, throwing theflow readings off.

The flow pickups may have multiple ports to get an average of pressures.If duct inlet conditions are less than optimal and flow is not uniform,the maximum flow reading can be adjusted to be more accurate using aflow coefficient. Note the calibration adjustment can take place only atone flow reading and this is always maximum airflow. This means that atall other readings the pickup & transducer combination calculate may beslightly inaccurate; the modulating closed loop control will adjust theair flow to a flow that is necessary to thermodynamically balance thetemperature of the room. Various air volumes of interest may include amaximum, minimum, and zero volume.

In other aspects, horizontal or diagonal set of pipes may be used tosample air pressures. Furthermore, a relationship between ΔP and CFM(LPM) may be plotted. There is no intrinsic difference betweenmultiplying √ΔP by C and multiplying ΔP by C² before taking the squareroot. However, if C is large, there is a big difference in the scale atwhich the controller performs the multiplication and the square root.

$\begin{matrix}{{Total}\mspace{14mu}{Air}\mspace{14mu}{Volume}\mspace{14mu}{Calculation}} & \; \\{{CFM} = {{Flow}\mspace{14mu}{Coefficient} \times 4004 \times \left. \sqrt{}\Delta \right.\; P \times {Duct}\mspace{14mu}{Area}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

Flow pickup flow may be increase the smallest measurable flow rate.Consequently, the Flow Coefficient, which adjusts for the flow pickupgain, may be a fraction less than one and the reciprocal of the pickupgain or slope.

Air Velocity Transducers

It is contemplated that the LFFC described herein can be used inconjunction with various sensor technologies in HVAC applications. Thesensors may be connected to a standalone transducer, such as devicesmade by Setra. It is contemplated that any transducer can be used inconjunction with the HVAC controls. Merely by way of example, a PCBmounted transducer may be used in HVAC systems.

Controller I/O Scanning Times

The controller utilized in conjunction with the LFFC 100 may scan, i.e.make A/D to conversions, once a second. Analog input data may be updatedonce a second. Loop calculation rates may also be made at the same rate.The rate at which the controller calculates the loop outputs maydirectly affect the size of the gain parameters. It is contemplated thatloop output calculation is scheduled on regular intervals to enhancecontroller performance.

Air Velocity Averaging & Electrical Noise Concerns

Air velocity readings may vary widely. Readings can be averaged toobtain consistent control action. In some aspects, this may beaccomplished by using a 4 byte (or 10 bit), or 8 byte adding FIFObuffer, and then performing a 2 or 3 step bit rotate to divide thenumber by 4 or 8. This method may average the data, with new incomingdata and old data rotating out. If performing the averaging in a highlevel programming language in decimal format, it is contemplated thatthe following equation may be used.

     μ = Σ Air  Velocity  Readings  (FIFO)/(Number  of  measurements)Averaging  Algorithm  used  with  Air  Velocity  Measurements  to  smooth  turbulent  readings

Electrical noises in the room temperature readings may disturb controlaction. When a large step change goes through the P equation, thecontrol loop proportional gain multiples the 20 step and the controllerremembers the change in subsequent calculations. It is contemplated thatgood A/D conversions and freedom from spurious electrical noise areimportant. Such conversions should be consistently reliable, with allcommon mode 60 Hz noise removed. Well-designed instrumentationamplifiers may guarantee clean, noiseless A/D conversions.

Controller Hardware RS 485 Twisted Pair Galvanic Isolation NetworkInterfaces

RS 485 refers to a transmission standard that uses differential voltagesto code transmission data for multipoint, multi-drop LAN systems. RS 485is the de facto standard for HVAC Building Automations System LANnetworks.

Many semiconductor manufacturers make RS 485 interface chips that followsimilar industry guidelines. Equation 10 below may describe a RS 485chip Common Mode Voltage rejection ratio. The RS 485 maximum Vcmrejection is specified as −7V to +12V.

$\begin{matrix}{\mspace{79mu}{{RS485}\mspace{14mu}{Hardware}\mspace{14mu}{Interface}\mspace{14mu}{Electrical}\mspace{14mu}{limits}}} & \; \\{{Vcm} = {{Vos} + {Vnoise} + {{Vgpd}\mspace{14mu}\left( {{Ref}:{{National}\mspace{14mu}{Semiconductor}}} \right)}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

This equation shows that if any of the above parameters exceed −7V to+12V, the chip fails to remove common mode noise. A key parameter whendiscussing galvanic isolation is Vgpd or voltage ground potentialdifference. Anytime the grounds between successive LAN nodes exceed thespecified limits, the network fails. Nodes can be separated by thousandsof feet. In cases when a 24 VAC is miswired, the controller may beforced to be 24 VAC above ground and cause network failure. To alleviateproblems, using a transformer or a DC to DC converter may galvanicisolate the RS 485 interface. It may further keep RS 485 chips fromburning due to wiring faults.

Triac Motor Driver Circuitry and Protection, Different Vendor Products

It is contemplated that pressure independent controls may be operatedwith actuators having interfaces called 3 point or floating modulating.One such actuator may be a Belimo actuator that is double insulated. Infloating point control, the controller microprocessor sends the actuatorto full close by sourcing 24V AC to the CW or CCW wires. Only one wirecan be energized at a time. Energizing both wires at the same timecauses the actuator to freeze and heat up. One wire rotates the actuatorin one direction and one rotates the actuator in the other direction.The percentage the damper blade moves may be determined by a run time of24V is applied to the CW or CCW wire. Direction is reversed by applyingsignal to the other wire. Direct action refers to actuator movement thatopens the damper when temperature increases. Reverse action refers toactuator movements that closes the damper when temperature increases.

Tabulated below are representative actuator manufacturers' data. The keyitem in the table is the actuator run time. For a controller toaccurately calculate damper blade percentage open, the controller can beconfigured to the correct run time. Generally, operation in the 60second time frame is preferred. Faster actuation may be used inlaboratory control. For instance, the 35 second actuator below is alaboratory actuator and is used on VAV controllers for pressurizinglaboratories.

TABLE 2 Possible Actuator Motor Specifications Manufacturer Product NoTorque Running Time Belimo LM24 45 in-lbs. (5.08 Nm) 95 seconds BelimoLM24 35 in-lbs. (3.05 Nm) 35 seconds Siemens GDE 44 in-lbs (4.79 Nm) 108seconds  JCI M9104 35 in-lbs (3.05 Nm) 60 seconds

UL Specifications, UL916 Low Voltage Regulating Equipment

UL916 is the standard of choice for building controls. UL916 is for lowvoltage regulating equipment or control equipment that energizes orde-energizes electrical loads to achieve a desired use of electricalpower. The equipment is intended to control electrical loads byresponding to sensors or transducers monitoring power consumption, bysequencing, by cycling the loads through the use of preprogrammed datalogic, circuits, or any combination 10 thereof. Summarized below are thekey design concerns related to UL compliance:

PCB digital output traces thickness in ounces of copper, width andseparation to adjacent traces. Class 2 transformers, PC mounted relays,PCB manufacturer; plastic molder all can be UL recognizedcomponents/manufacturers.

Plastic material used in the plenum air space, 94-VO flame retardantepoxy.

Mixing NEC Class 1 line voltage with Class 2 low voltage in sameenclosures.

UL Specifications, UL864 Smoke Control

The products covered by this UL standard are intended to be used incombination with other appliances and devices to form a commercial firealarm system. These products provide all monitoring, control, andindicating functions of the system. The criteria for compliance withthis standard are significantly higher than UL916 and involve all thecomponents that make up a system. For an LFFC and/or LFFC incorporatedin a Zone Control Unit (“ZCU”) to comply with this standard, thecontroller, metal enclosure, transformers and wiring can form a completeapproved solution. An UL864 compliant ZCU may fit into an entire controlsystem with other hardware, software and mechanical components to form acommercial fire alarm smoke control system.

UL tests cover life safety issues and functionality of the testeddevice. In that regard, UL tests may force fundamental design decisionsand tradeoffs to be made prior to a product becoming manufacturingready. To comply with this standard, the “Controller under Test” shouldpass the test described in Section C.

Opportunities in a Segmented Industry where Equipment and Controlsremain Separate It is contemplated that the LFFC described herein and/orthe central system may be controlled electronically with Direct DigitalControl (DDC) or with pneumatic (air) control systems. Digital systemsare computer controlled systems that can employ sophisticatedcalculations and algorithms to implement control sequences. Pneumaticsystems use air signals to change control sequences. As mentionedearlier, pressure independent refers to controller ability to measureair flow and ride through system variations that result when differentzones within the building put different loads on the heating and coolingsystem.

Digital control systems have many advantages. They do not requirefrequent calibration, last longer, and do not require air compressorsequipped with special air dryers and lubrications systems. DDC systemscan perform complex calculations and sequences. DDC systems can receiveinstructions from a master computer and share data with multipleoperators located anywhere with a Web interface. Further, DDC systemstransmit to master front end computers information such as damper andvalve position, room temperature, supply air quantity, and supply airtemperature.

Multi-zone AHU System

The LFFC described herein may be used in a central air, or a multi-zonesystem that meets the varying needs of multiple and different zoneswithin larger buildings. Such systems may be a mix of centralized andzone HVAC equipment. Multi-zones have a separate supply air ducts toserve each zone in a building. There is a heating and cooling water(glycol and water used interchangeably) coil in the central air handlingunit.

Variable Air Volume Systems

The LFFC 100 described herein may be utilized in a variable air volume(VAV) system to be more energy efficient and to meet the varying heatingand cooling needs of different building zones. A zone may be a singleroom or cluster of rooms with the same heat gain and heat losscharacteristics. Such a VAV system can save at least 70 percent inenergy costs as compared to conventional systems. In addition, it iscontemplated that the LFFC 100 is economical to install and to operate.In some embodiments, the system utilizes 55° F. (10° C.) primary air.Room thermostats may control the amount of primary air delivered to eachzone through LFFC's for each zone. Such dampers may vary the volume ofair to each zone according to the cooling needs.

In some aspects, the fan CFM output may be varied according to the totalneed of the zones. The fan may be sized with diversity ˜90% of worstcase load. As the air volume for the zones vary, the static pressure(SP) in the main duct may vary. In legacy systems with VAV boxesrequiring 1″ SP to operate, an SP sensor in the main duct controlled thefan output to maintain that constant supply duct static pressure. Withentire elimination of VAV boxes in favor of LFFC's, this is no longerrequired or desirable. With use of LFFC's throughout a building, nominimum supply pressure is maintained. Fans are controlled by the needsof the LFFC's. These systems may be variable volume, constanttemperature. In some systems that provide cooling only, a separatesource of heat may be utilized as needed for outer rooms. This may besupplied by perimeter heating in the rooms. Other units in the systemmay include a water coil and control valve to provide heating. A bigadvantage of VAV systems that utilize the LFFC described herein is thatthey are able to meet the comfort requirements of different zones in abuilding without heating and cooling at the same time. Under somecircumstances short alternating periods of central heating and coolingmay be employed, with tight synchronization of fan and LFFC controlmodes.

Varying Central Supply Air Fan

It is contemplated that the volume (CFM/LPM) of primary air delivered bythe central air handling unit can vary according to the demands of theindividual units containing the LFFC's in the system. In this way, thesupply fan in the central air handling unit may vary its output in orderto meet the needs of all the units. The task of the central fancontroller is to keep all LFFC's satisfied while not overpressurizingthe system so that all LFFC's would have to feather to hold back theexcess pressure. The system is balanced while all LFFC's are satisfiedand at least one LFFC is fully open. Without this last simple conditionfan operating point is not well defined: it might run wide open, wastinga tremendous amount of energy and creating tremendous noise at thenearly tightly closed LFFC's.

Applications of the LFFC in Burners and Boilers

It is contemplated that the LFFC described herein may be utilized forburner boiler fluid control. Merely by way of example, the LFFC can beutilized in a large fire tube boiler, which can mix natural gas and airin the burner to produce a flame that converts water to steam. The steammay be used to heat buildings and industrial processes. Large equipmentefficiencies are important, since small changes in efficiency translateinto large changes in fuel input. Therefore, the LFFC can be applied forhigh turndown air control in burner boilers.

In particular, new energy efficiency standards drive burner boilermanufacturers toward O₂ trim control. In O₂ trim control, burner exhaustgas O₂ concentrations are monitored and used to modulate gas and supplyair to obtain the highest efficiency air/fuel mixture or Stoichiometricratio. Tracking controls proportion fuel and air ratios by applying theBernoulli equation. As combustion air and gas flow change throughmetering devices, air pressure changes with the square of air and/or gasvelocity. The blower and damper are adjusted together. It iscontemplated that the LFFC be applied to both the air blowers and fuelmetering valves to more precisely meter air into the combustion chamberand allow boiler to throttle down further. The LFFC may be usedalternatively or in combination with linkage-less actuators that arecurrently used in burner boilers.

It is noted that CFM measurement may not be required from the LFFC inburner boiler applications. Rather, the LFFC provides high turndownresolution on both the air and fuel side. The combustion controllerfrequently does not need to calculate the mass air flow rate and simplypositions the damper so the control feedback variable, O₂ approaches theset point value.

INDUSTRIAL APPLICABILITY

The LFFC described herein has application in any industrial sector thatmeasures and throttles air or fluids. Such industrial sectors mayinclude, but are not limited to: Biotechnology and drugs, Hospitals andHealthcare, Laboratories and Pharmaceuticals, Pollution and TreatmentControls, Water Utilities, Treatment and Filtration, SelectedManufacturing Industries, Semiconductor fabrication, Mining and Metals,Data Centers, and Diversified Machinery and Farming.

It is contemplated that multiple industrial applications are possiblefor the LFFC due to the accurate turndown of the damper design, advancedfirmware, and software integration. For example, the LFFC can be used indevices for controlling multiple zones through multiplexing of damperscommensurate to thermal conductivity requirements and resetting ofancillary equipment such as fans, pumps, chillers and boilers at thezone level or system level. Localized zone heating and cooling nowbecomes affordable as several devices are being incorporated into one.This permits shutting down or going to minimum set points in unoccupiedzones, thus conserving energy and maintaining IAQ and occupant comfort.The high turndown and accurate flow measurement makes the LFFC a naturalintegration into process type applications and refineries where anaccurate air fuel mixture is commonly required resulting in increasedproductivity and reduced energy costs. The LFFC can be made out ofvarious materials for caustic environments and various ancillarycomponents such as sensing elements, transducers, firmware and software.

It is contemplated that the invention disclosed herein provides for adevice that measures and regulates high and very low volumes of airand/or fluid flows with precision, inexpensively and with superioracoustics and greatly reduced energy consumption. The disclosure alsoprovides for a high turndown device that permits use at lowervelocities, greatly reducing noise generation and eliminating the needfor sound-attenuating liners such as fiberglass and double walls.Further, the disclosure provides for a high rangeability device thatallows streamlining product portfolios by combining several product partnumbers into much smaller number of offerings. In another aspect, thedisclosure provides for an inexpensive device that allows equipment tobe scaled back 100-1 or higher, rather than legacy 5-1, which leads toenergy savings, fewer product variations simpler and more robustapplication designs. Still further, the disclosure provides for a devicethat provides better fluid, air volume and water temperature control,while conserving more energy, employing a fundamentally simpler designand meeting all new and old building fresh air, comfort and energycodes. The disclosure is also directed to a device that can beengineered, selected, and sized without sophisticated software programs.

Related Device, System, and Method Embodiments

FIG. 12 depicts aspects of a fluid system 1200 according to embodimentsof the present invention. As depicted here, system 1200 can include adevice for measuring and controlling a fluid flow. In some cases, thefluid flow can be through a flow pathway in a duct 1202 of a heating,ventilation, and air conditioning (HVAC) system. The device can includean orifice plate 1204 positioned within the flow pathway and defining avariable opening Ao for receiving flow there through. In some cases, thesystem or device can include an actuator assembly 1206 in operativeassociation with the orifice plate 1204. As shown here, the system ordevice can also include a controller 1208 in operative association withthe actuator assembly 1206, orifice plate 1204, or both. The controller1208 can include a processor, and a memory communicatively coupled withand readable by the processor. Further, the controller memory caninclude stored processor-readable instructions that, when executed bythe processor, cause the processor to determine a pressure differentialbetween upstream and downstream sensors. In some cases, the instructionscause the processor to determine a position, configuration, ororientation of the plate 1204 (or components thereof), for example basedon a position feedback received from the actuator assembly 1206. In somecases, the instructions cause the processor to operate the actuatorassembly 1206 so as to regulate the variable opening A_(o) based on thepressure differential and the position, orientation, or configuration ofthe plate 1204.

According to some embodiments, processor-readable instructions, whenexecuted by the processor, cause the processor to determine one or moreof (i) the sensor pressure differential, (ii) a variable opening area Aodefined by the damper assembly or plate 1202, (iii) a flow coefficientMF, and (iv) a flow rate based on the pressure differential and the flowcoefficient.

In some cases, operation of the plate 1204, the actuator assembly 1206,an upstream fluid control and/or supply mechanism 1210, and/or adownstream fluid control mechanism 1212, as controlled by the controller1208, can be based on input received by the controller 1208 from auser/operator setting device 1214, the plate 1204, the actuator assembly1206, the 20 upstream fluid control and/or supply mechanism 1210, thedownstream fluid control mechanism 1212, the upstream sensor P₁, and/orthe downstream sensor P₂.

Embodiments of the present invention provide accurate flow measurementdevices and methods. For example, such techniques can allow for controlof fans which automatically saves 30 percent of energy in a building andsubstantially cuts part numbers and skews as one device has such a broadmeasuring range. Measuring accurately over such a wide range makes itmore efficient to control flow. In addition when only 20 CFM of outsideair is required in a zone the device can meter in exactly 20 CFM ofoutside air. Currently available VAV boxes cannot measure down below say300 CFM, so 280 CFM per zone needs to be re heated or re cooled thusunnecessarily loading the chillers and the boilers. Additional energysavings and better occupancy comfort are achieved.

THE HISTORY AND THEORY BEHIND THE LOW FLOW FLUID CONTROLLER (LFFC) I.The Vena Contracta

Torricelli observed (1643) that water issuing from a small hole in alarge tank contracts as it passes through the hole. Newton's attempts toquantify this discharge were unsuccessful until he too noticed thecontraction in the “vein” of issuing water. He called the phenomenon theVena Contracta, the name used to this day. He measured the contractedarea to be about half the orifice area, and published this in the 2^(nd)edition of his Principia (1713) as a correction to his earlier work.

In 1738 Bernoulli published his famous principle: SP+½ρν² is conservedalong (not necessarily across) flow streamlines In modern terminologyTP(total pressure)=SP(static pressure)+VP(velocity pressure) constant onstreamlines. So, if Δp is the difference in static pressure inside thetank (at the level of the opening but far away so the velocity can betaken as 0) vs outside the tank, then ½ρν²=Δp. Newton's Law ofconservation of momentum, applied to fluids, gives ρν²A_(c)=ΔpA_(o),A_(o) the area of the opening, for one unaware of the Vena Contracta.This contradicts the previous equation unless A_(o)=0: no “vein.” Bordanoticed (1760) that the momentum balance becomes ρν²A_(c)=ΔpA_(o), A_(c)the area of the contracted flow, when one takes the Vena Contracta intoaccount, and the contradiction disappears if

$\frac{A_{c}}{A_{o}} = {\frac{1}{2}.}$Unfortunately, this result was in conflict with contemporary directexperiment, which estimated

$\frac{A_{c}}{A_{o}}$to be between 0.60 and 0.64. This contradiction between nature and thelaws so recently won from nature has persisted for the past 250 years,standing in the way of deeper understanding of the orifice plate. Byenforcing the more recently exploited concept of continuity of pressure,which by Bernoulli's principle implies also continuity of velocity alongstreamlines, consistency between nature and nature's laws obtains for

$\frac{A_{c}}{A_{o}}$between 0.536 and 0.753. Values below 0.536; in particularNewton/Borda's 0.5, are not viable.

II. Reconciliation of Theory and Measurement

$\frac{A_{c}}{A_{o}} = \frac{{Area}\mspace{14mu}{of}\mspace{14mu}{contracted}\mspace{14mu}{stream}}{{{Area}\mspace{14mu}{of}\mspace{14mu}{orifice}} = {\pi\; r_{o}^{2}}}$

The model here is an infinite reservoir with a flat wall containing anorifice of area A_(o). For concreteness axisymmetric flow is consideredabout a circular hole of radius r_(o) (see FIG. 18A). Similar but weakerresults are obtainable for more general shapes. The flow is complex inthe area of the opening, but simple far upstream and beginning a shortdistance downstream of the hole. Upstream, at a radius r>>ro, the flowbecomes uniformly radial inward on concentric hemispheres:

$\begin{matrix}{{\left. v_{r}\rightarrow{- \frac{Q}{2\pi\; r\; 2}} \right.,{{{where}\mspace{14mu} Q\mspace{14mu}{is}\mspace{14mu}{the}\mspace{14mu}{total}\mspace{14mu}{flow}};}}{v_{\theta} = {v_{\varphi} = {{0.r} ⪢ r_{o}}}}} & (1)\end{matrix}$

(1) satisfies the incompressible Navier-Stokes equation in that region.Downstream of the Vena Contracta the flow is again simple: velocity is 0outside of A_(c), with uniform parallel flow (Velocity ν_(c)=Q/A_(c)) inthe z direction within A_(c) downstream of the region of contraction.

The contracting “veins” of water Torricelli, Newton, and Borda observedissuing into still air appeared very much like FIG. 1. Viscosity and, atthe indicated scale, gravity are not at issue here. With water issuinginto still water or air into air, viscosity soon diffuses away the shearboundary of the “vein” and the flow spreads in a generally turbulentfashion. Nonetheless, the contracted jet does persist over a sufficientdistance to validate the following analysis. z components of Force andMomentum Flux require balancing. The other components balanceautomatically in axisymmetric flow. The terms “Force and Efflux” willrefer here to respective components in the z direction in FIG. 1.

Although Bernoulli's equation applies individually to each streamline,all streamlines in the present flow arise from uniform still fluid atr=∞, so Total Pressure (TP) can reasonably be equated on allstreamlines. This can't be said for the still fluid downstream of theplate, which does not originate in the upstream reservoir, need not evenconsist of the same type of fluid, and will be seen to have a uniform TPless than the TP just defined for the flow originating upstream.

$\begin{matrix}{{{S_{1}\text{:}\mspace{14mu}{Efflux}} = {{- {\int_{S_{1}}{\rho\; v\; v_{z}d\; S}}} = {{{- {\rho\left( \frac{Q}{2\pi\; r_{1}^{2}} \right)}^{2}}\left( {2\pi\; r_{1}^{2}} \right){\int_{0}^{\pi/2}{\cos\;\theta\;\sin\;\theta\; d\;\theta}}} = {{- \left( \frac{\rho\; Q^{2}}{4\pi\; r_{1}^{2}} \right)}r_{1}}}}}\operatorname{>>}r_{0}} & \left( {2a} \right) \\{{{Force} = {{\int{S\; P_{1}\cos\;\theta\; d\; S}} = {{\left( {{T\; P} - {\frac{\rho}{2}\left( \frac{Q}{2\pi\; r_{1}^{2}} \right)^{2}}} \right)2\pi\; r_{1}^{2}{\int_{0}^{\pi/2}{\cos\;\theta\;\sin\;\theta\; d\;\theta}}} = {{T\; P\;\pi\; r_{1}^{2}} - {\left( \frac{\rho\; Q^{2}}{8\pi\; r_{1}^{2}} \right)r_{1}}}}}}\operatorname{>>}r_{0}} & \left( {2b} \right) \\{{S_{2}\text{:}\mspace{14mu}{Efflux}} = {{\rho\; V_{c}^{2}A_{c}} = {\rho\frac{Q^{2}}{A_{c}}}}} & (3)\end{matrix}$

Forces on S₂ and downstream face of S_(o) balance for r>=r₀, leaving

$\begin{matrix}{\mspace{79mu}{{{net}\mspace{14mu}{Force}} = {{{- {SP}_{c}}A_{o}} = {{{- \left( {{TP} - {\frac{\rho}{2}\left( \frac{Q}{A_{c}} \right)^{2}}} \right)}A_{o}\mspace{14mu}{for}\mspace{14mu} r} < {r_{0}.}}}}} & (4) \\{\mspace{79mu}{{S_{o}\text{:}\mspace{14mu}{Force}\mspace{14mu}{of}\mspace{14mu}{upstream}\mspace{14mu}{face}\mspace{14mu}{of}\mspace{14mu}{plate}} = {{- {\int{SPdS}_{0}}} = {{- {\int_{r_{o}}^{r_{1}}{\left( {{TP} - {\frac{\rho}{2}v_{r}^{2}}} \right)2\pi\;{rdr}}}} = {{- {{TP}\left( {{\pi\; r_{1}^{2}} - {\pi\; r_{0}^{2}}} \right)}} + {\frac{\rho}{2}{\int_{r_{0}}^{r_{1}}{v_{r}^{2}2\pi\;{{rdr}.}}}}}}}}} & (5)\end{matrix}$

TP terms cancel, as they must, leaving

$\frac{1}{r_{1}^{2}}$terms which drop out when r_(1→∞).

$\frac{\rho\; Q^{2}}{2}$will then factor out of remaining terms, if −ν_(r) is written as

${\frac{Q}{2\;\pi\; r^{2}}\left( {1 + f} \right)\text{:}\mspace{14mu}\begin{matrix}\left. f\rightarrow 0 \right. \\\left. r\rightarrow\infty \right.\end{matrix}},\mspace{31mu}{v_{r} \approx {- \frac{Q}{4\;\pi\; r^{2}}}}$asymptotically for r>>r₀, but continuity of v along the constantvelocity, constant pressure streamlines issuing downstream from theorifice edge requires

${- {v_{r}\left( r_{0} \right)}} = {v_{c} = {{\frac{Q}{A_{c}} > \frac{Q}{2\;\pi\; r_{o}^{2}}} = {\frac{Q}{2\; A_{o}} \cdot {\left( {{\frac{A_{c}}{2\; A_{o}} \approx \frac{.62}{2}} = {.31}} \right).}}}}$Setting

${f\left( a_{o} \right)} = {\frac{2\;\pi\; r_{o}^{2}}{A_{c}} - 1}$accomplishes this.

$\begin{matrix}{\mspace{79mu}{{v_{r}^{2} = {\left( \frac{Q}{2\;\pi\; r^{2}} \right)^{2} + {\left( \frac{Q}{2\;\pi\; r^{2}} \right)^{2}{f\left( {2 + f} \right)}}}},{and}}} & \; \\{{{\left. {{\frac{\rho}{2}{\int_{r_{o}}^{r_{1}}{v_{r}^{2}2\;\pi\; r\;{dr}}}} = {{{\frac{\rho\; Q^{2}}{2}{\int_{r_{o}}^{r_{1}}{\left( \frac{1}{2\;\pi\; r^{2}} \right)^{2}2\;\pi\; r\;{dr}}}} + {\frac{\rho\; Q^{2}}{2}{\int_{r_{o}}^{r\; 1}{\left( \frac{1}{2\;\pi\; r^{2}} \right)^{2}f\left( {2 + f} \right)2\;\pi\; r\;{dr}}}}} = {{{\frac{\rho\; Q^{2}}{2}{\int_{r_{o}}^{r_{1}}{\frac{1}{2\;\pi}r^{- 3}{dr}}}} + {\frac{\rho\; Q^{2}}{2}{\int_{r_{o}}^{r_{1}}{\frac{1}{2\;\pi}r^{- 3}{f\left( {2 + f} \right)}{dr}}}}} = {\frac{\rho\; Q^{2}}{2}\frac{1}{2\;\pi}\frac{r^{- 2}}{- 2}}}}} \right\rbrack\begin{matrix}{r\; 1} \\\;_{r_{o}}\end{matrix}} + {\frac{\rho\; Q^{2}}{2}{\int_{r_{o}}^{r\; 1}{\frac{f\left( {2 + f} \right)}{2\;\pi\; r^{2}}{dr}}}}} = {{\frac{\rho\; Q^{2}}{2}\left( {\frac{1}{4\;\pi\; r_{o}^{2}} - \frac{1}{4\;\pi\; r_{1}^{2}}} \right)} + {\frac{\rho\; Q^{2}}{2}{\int_{r_{o}}^{r\; 1}{\frac{f\left( {2 + f} \right)}{2\;\pi\; r^{2}}{{dr}.}}}}}} & (6)\end{matrix}$

See FIG. 18B.

Note:

${{f\left( a_{o} \right)}\left( {2 + {f\left( a_{o} \right)}} \right)} = {{\left( {\frac{2\;\pi\; r_{o}^{2}}{A_{c}} - 1} \right)\left( {\frac{2\;\pi\; r_{o}^{2}}{A_{c}} + 1} \right)} = {{\left( \frac{2\;\pi\; r_{o}^{2}}{A_{c}} \right)^{2} - 1} = {\left( \frac{2\; A_{o}}{A_{c}} \right)^{2} - 1.}}}$

Letting r_(1→∞) now and factoring out

$\frac{\rho\; Q^{2}}{2},$the force-efflux balance becomes

$\begin{matrix}{{\frac{A_{o}}{A_{c}^{2}} + \frac{1}{4\; A_{o}} + {\int_{r_{o}}^{\infty}{\frac{f\left( {2 + f} \right)}{2\;\pi\; r^{2}}{dr}}}} = {\frac{2}{A_{c}}.}} & (7)\end{matrix}$

1) Multiplying through by

${{{A_{o}\text{:}\mspace{14mu}\left( \frac{A_{o}}{A_{c}} \right)^{2}} - {2\left( \frac{A_{o}}{A_{c}} \right)} + \frac{1}{4} + {A_{o}{\int_{r_{o}}^{\infty}{\frac{f\left( {2 + f} \right)}{2\;\pi\; r^{2}}{dr}}}}} = 0},$and 2) passing to a dimensionless variable

${x = {\frac{A_{o}}{\pi\; r^{2}} = {{\left( \frac{r_{o}}{r} \right)^{2}\mspace{14mu}{so}\mspace{14mu}{dx}} = {{- \frac{2\; A_{o}}{\pi\; r^{2}}}{dr}}}}},$put this into dimensionless form:

$\begin{matrix}{{\left( \frac{A_{o}}{A_{c}} \right)^{2} - {2\left( \frac{A_{o}}{A_{c}} \right)} + \frac{1}{4} + {\frac{1}{4}{\int_{0}^{1}{{f\left( {2 + f} \right)}{dx}}}}} = 0} & (8)\end{matrix}$

See FIG. 18C.

$\frac{Q}{2\;\pi\; r^{2}}$represents the lowest order (n=0; mass flow) term in an expansion of theaxisymmetric potential flow in the upstream infinite hemisphere usingharmonic potentials

$\varphi_{2_{n}} = {\frac{P_{2n}\left( {\cos\;\theta} \right)}{r^{{2\; n} + 1}}.}$The even order Legendre Polynomials P_(2n)(cos θ) form an orthogonalbasis on

$\left\lbrack {0,\frac{\pi}{2}} \right\rbrack,$and the flow terms ∝∇φ_(2n) give radial velocities

$\frac{c}{r^{{2n} + 2}}$along the boundary

${\theta = \frac{\pi}{2}};$the upstream surface of the orifice plate. Take

$\begin{matrix}{{f_{n} = {{\left( {\frac{2A_{o}}{A_{c}} - 1} \right)\left( \frac{r_{o}}{r} \right)2n} = {\left( {\frac{2A_{0}}{A_{c}} - 1} \right)x^{n}\mspace{14mu}{there}}}},{{{so} - V_{r}} = {\frac{Q}{2A_{o}}{x\left( {1 + {\left( {\frac{2A_{o}}{A_{c}} - 1} \right)x^{n}}} \right)}}},{{{so}\mspace{14mu}\frac{1}{4}{\int_{0}^{1}{{f_{n}\left( {2 + f_{n}} \right)}{dx}}}} = {{\left( \frac{A_{o}}{A_{c}} \right)^{2}\frac{1}{{2n} + 1}} + {\left( \frac{A_{o}}{A_{c}} \right)\left( {\frac{1}{n + 1} - \frac{1}{{2n} + 1}} \right)} - {\frac{1}{4}\left( {\frac{1}{n + 1} - \frac{1}{{2n} + 1}} \right)}}},{{{so}\mspace{14mu}(8)\mspace{14mu}{becomes}\mspace{14mu}\left( \frac{A_{o}}{A_{c}} \right)^{2}\left( {1 + \frac{1}{{2n} + 1}} \right)} - {2\frac{A_{o}}{A_{c}}\left( {1 - \frac{.5}{n + 1} + \frac{.5}{n + 1}} \right)} + {\frac{1}{4}\left( {1 - \frac{2}{n + 1} + \frac{1}{{2n} + 1}} \right)}},{and}} & (9) \\{\frac{A_{c}}{A_{o}} = \frac{1 + \frac{1}{{2n} + 1}}{\begin{matrix}{1 - \frac{.5}{n + 1} + \frac{5}{{2n} + 1} +} \\\sqrt{\left( {1 - \frac{.5}{n + 1} + \frac{.5}{{2n} + 1}} \right)^{2} - {\frac{1}{4}\left( {1 + \frac{1}{{2n} + 1}} \right)\left( {1 - \frac{2}{n + 1} + \frac{1}{{2n} + 1}} \right)}}\end{matrix}}} & (10)\end{matrix}$

-   -   Values of the contraction coefficient

$\frac{A_{c}}{A_{o}}$using a single higher order φ_(2n) are plotted in a table at right. Thelower limit 0.536 is rigorous and obtainable independently and for moregeneral orifice shapes, without recourse to the axial symmetry and zonalharmonics employed above. The upper limit 0.753, on the other hand, isdependent on a single higher harmonic φ_(2n), together with the φ₀ term,dominating the flow. A more complex model giving values to nonzerocoefficients for more, possibly all, of the φ_(2n) would be needed tofurther narrow the range of, or possibly completely define,

$\frac{A_{c}}{A_{o}}.$As it is, including more zonal harmonics just fills in

$\frac{A_{c}}{A_{o}}$between the Table 1 values and also a bit above 0.753.

TABLE 1 n $\frac{A_{c}}{A_{o}}$ 1 .753 2 .675 3 .638 4 .617 5 .603 6.593 7 .585 8 .58  ↓ ↓ ∞ .536

Kirchoff, 1869, found 0.611 rigorously for an orifice in the form of aninfinite slot.

The above stands as a limiting case of ducted orifice plates for

$\left. \frac{A_{o}}{A_{d}}\rightarrow{0\mspace{14mu}{\left( {{duct}\mspace{14mu}{area}\mspace{14mu} A_{d}}\rightarrow\infty \right).}} \right.$A similar analysis applies for finite A_(d).

III. Ducted Orifice Plates

The ducted orifice plate has been a standard device for measuring fluidflow for well over 100 years. For an orifice in a duct the contractionratio

$\frac{A_{c}}{A_{o}}$cannot remain constant at the often assumed values of 0.61 or 0.62 as

$\frac{A_{o}}{A_{d}} = {\left. \frac{{orifice}\mspace{14mu}{area}}{{duct}\mspace{14mu}{area}}\rightarrow{1\text{:}\mspace{14mu}{at}\frac{A_{o}}{A_{d}}} \right. = 1}$there is no orifice plate, so

$\frac{A_{c}}{A_{o}}$must=1 also. In 1872 Weisbach summarized contemporary experimentalresults in the correlation

$\begin{matrix}{\frac{A_{c}}{A_{o}} = {{.62} + {{.38}\mspace{11mu}{\left( \frac{A_{o}}{A_{d}} \right)^{3}.}}}} & (11)\end{matrix}$

Test (11) and similar expressions for compatibility with z-force andmomentum and mass flux balance:

$\begin{matrix}{{{{On}\mspace{14mu} S_{1}},{{z\text{-}{flux}} = {{- \rho}\; V_{d}^{2}A_{d}\mspace{230mu}{See}\mspace{14mu}{{FIG}.\; 18}D}}}{{{On}\mspace{11mu} S_{2}},{{z\text{-}{flux}} = {{\rho V}_{c}^{2}A_{c}}}}{{{On}\mspace{14mu} S_{1}},{{z\text{-}{force}} = {{{SP}_{d}A_{d}} = {{TPA}_{d} - {\frac{\rho\; v_{d}^{2}}{2}A_{d}}}}}}} & \;\end{matrix}$

TP and velocity may be taken constant across streamlines far upstream,with duct face velocity v_(d). The periphery of the upstream surface ofthe orifice plate is a stagnation zone: V=0, so SP=TP−0=TP there. Thevelocity along the upstream face increases to V_(c) as it nears the edgeof the opening, so SP drops from TP to TP−VP_(c) at the edge.

For r>r_(o) forces in the back of the orifice plate and at S₂ are inbalance, leaving net force

${- {SPA}_{o}} = {{- \left( {{TP} - {\rho\frac{v_{c}^{2}}{2}}} \right)}{A_{o}.}}$For duct radius r_(d)>>r_(o), there is a region of radial flow

${v_{r} \approx {- \frac{Q}{2\pi\; r^{2}}}},$with departures near r=r_(o) and r=r_(d).

See FIG. 18E.

f_(n) satisfying conditions at r=r_(o), or

$x = {\left( \frac{r_{o}}{r} \right)^{2} = 1}$were developed above. Now 1+f must vanish at the stagnation point r_(d),where the plate meets the duct at 90°. We plot the (1+f)² and (1+f_(n))²integrands in FIG. 18F. Find x_(o)s·t·∫_(x) _(o) ¹(1+f_(n))²=∫_(A) _(o)_(/A) _(d) ¹(1+f)².

This permit replacing the lower limit of integration 0 in (8) withx_(o), which evaluates to an even less tractable sequel to (10):

$\begin{matrix}{\frac{A_{c}}{A_{o}} = {\frac{1 + \frac{1 - x_{o}^{{2n} + 1}}{{2n} + 1}}{\begin{matrix}{1 - \frac{1 - x_{o}^{n + 1}}{2\left( {n + 1} \right)} + \frac{1 - x_{o}^{n + 1}}{2\left( {n + 1} \right)} +} \\\sqrt{\left( {1 - \frac{1 - x_{o}^{n + 1}}{2\left( {n + 1} \right)} + \frac{1 - x_{o}^{n + 1}}{2\left( {n + 1} \right)}} \right)^{2} - {\left( {1 + \frac{x_{o}^{{2n} + 1}}{2n\;\pi}} \right)\left( {\frac{1 - x_{o}}{4} - \frac{1 - x_{0}^{n + 1}}{2\left( {n + 1} \right)} + \frac{1 - x_{o}^{{2n} + 1}}{4\left( {n + 1} \right)}} \right)}}\end{matrix}}.}} & (12)\end{matrix}$

x_(o) is not constant: it must catch up with

$\left. {\frac{A_{o}}{A_{d}}\mspace{14mu}{as}\mspace{14mu}\frac{A_{o}}{A_{d}}}\rightarrow 1 \right.$and the integral vanishes. A natural choice for this function,

${x_{o} = {\frac{A_{o}}{A_{d}}\left( {ɛ + {\left( {1 - ɛ} \right)\frac{A_{o}}{A_{d}}}} \right)}},$yields a good match between Weisbach's curve and A_(c)/A_(o) from (12),with ε=0.2 and n=4. (With this crude model, just bounding curves alittle above and below Weisbach's were anticipated. Instead, a nearperfect match emerged.)

With these results in hand, examination of orifice plate flow/dischargecoefficients can proceed.

IV. The Flow Coefficient

Bernoulli's Principle relates velocities and pressures alongstreamlines: at arbitrary points 1 and 2 on any streamline,

$\begin{matrix}{{{SP}_{1} + {\rho\frac{v_{1}^{2}}{2}}} = {{SP}_{2} + {\rho{\frac{v_{2}^{2}}{2}.}}}} & (13)\end{matrix}$

For flow uniform across areas A₁ and A₂ enclosing the same bundle ofstreamlines, and with Q the common total flow through the A_(i), (13)becomes

$\begin{matrix}{{\Delta\; P} = {{{SP}_{1} - {SP}_{2}} = {{{\frac{\rho}{2}\left( \frac{Q}{A_{2}} \right)^{2}} - {\frac{\rho}{2}\left( \frac{Q}{A_{1}} \right)^{2}}} = {\frac{\rho\; Q^{2}}{2}\left( {\frac{1}{A_{2}^{2}} - \frac{1}{A_{1}^{2}}} \right)}}}} & (14)\end{matrix}$(14) expresses differences in static pressure as a function of Q² and acoefficient with dimensions

$\frac{1}{A^{2}}.$It rearranges directly into an expression of Q in terms of pressuredifferences:

$\begin{matrix}{Q = \frac{\sqrt{\frac{2\Delta\; p}{\rho}}}{\sqrt{\frac{1}{A_{2}^{2}} - \frac{1}{A_{1}^{2}}}}} & (15)\end{matrix}$

It is common to redefine (15) in terms of flow through a reference areaA_(o) and a dimensionless constant, here called C_(F). Multiplying anddividing by A_(o) in (15), gives

$\begin{matrix}{{Q = {\frac{A_{o}\sqrt{\frac{2\Delta\; p}{\rho}}}{\sqrt{\left( \frac{A_{o}}{A_{2}} \right)^{2} - \left( \frac{A_{o}}{A_{1}} \right)^{2}}} \equiv {C_{F}A_{o}\sqrt{\frac{2\Delta\; p}{\rho}}}}},} & \left( {16a} \right) \\{C_{F} = {\frac{1}{\sqrt{\left( \frac{A_{o}}{A_{2}} \right)^{2} - \left( \frac{A_{o}}{A_{1}} \right)^{2}}}\mspace{14mu}{the}\mspace{14mu}{Flow}\mspace{14mu}{{Coefficient}.}}} & \left( {16b} \right)\end{matrix}$(16) is immediately applicable to any inviscid system in which the sameflow passes uniformly through at least 2 distinct areas A₁ and A₂.

$\sqrt{\frac{2\Delta\; p}{\rho}}$has the dimensions of a velocity: multiplied by A_(o), it can be thoughtof as the mean flow through that area. The physical system being modeledmay not actually possess a section of area equal to the reference A_(o),and in case A_(o) does refer to a physical location in the system, theflow need not be uniform or even measurable there. A_(o) may refer toone of the actual measurement areas A₁ or A₂; in the case nextconsidered, it does not.

IVA The Orifice Plate Discharge Coefficient

Something like (16) is widely used with a great variety of flowmeasuring devices, along with tables and graphs of the flow coefficientC_(F), or the related discharge coefficient C_(d). In families ofdevices in which the areas A₁ and A₂ may approach arbitrarily closely toeach other, C_(F) graphs can never be complete: C_(F)=∞ if A₁=A₂. Fororifice plates, particularly in the US, a variant of (16) has beendeveloped in which the explosive behavior as A₂→A₁ has been factoredout.

FIG. 4A illustrates a typical orifice plate tap arrangement. Thedownstream tap is located just downstream of the plate, where itmeasures still air at essentially SP_(c), the static pressure in thecontracted stream. (In still air, SP is constant, and by continuity ofpressure, must equal the constant pressure P_(c) in the contractedstream.) The upstream tap measures SP_(d) in the undisturbed flow at afixed distance upstream of the plate. A_(o) is the area of the orificeitself. (16) becomes

$\begin{matrix}{Q = {\frac{A_{o}\sqrt{\frac{2\Delta\; p}{\rho}}}{\sqrt{\left( \frac{A_{o}}{A_{c}} \right)^{2} - \left( \frac{A_{o}}{A_{d}} \right)^{2}}} = {{C_{F}A_{o}\sqrt{\frac{2\Delta\; p}{\rho}}\text{:}\mspace{14mu} C_{F}} = {\frac{1}{\sqrt{\left( \frac{A_{o}}{A_{c}} \right)^{2} - \left( \frac{A_{o}}{A_{d}} \right)^{2}}}.}}}} & (17)\end{matrix}$

The variant is

$\begin{matrix}{Q = {\frac{C_{d}A_{o}}{\sqrt{1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}}}\sqrt{\frac{2\Delta\; p}{\rho}}}} & (18)\end{matrix}$which has been the standard form in the US since at least 1930(Johansen). (18) differs markedly from (17), and appears to have notheoretical foundation. It is extremely useful and successful, however!The measured Coefficient of Discharge C_(d) varies little between

$\frac{A_{o}}{A_{d}} = 0$and 0.5, and by only about 10% on [0,1]. Yet it appears to arise fromignoring the Vena Contracta, so

$\left( \frac{A_{o}}{A_{c}} \right)^{2}$is replaced by 1 in (17), then bringing in C_(d) as a correction factorto make it work. But it works superbly well! (17) and (18) give

$\begin{matrix}{C_{d} = \sqrt{\frac{1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}}{\left( \frac{A_{o}}{A_{c}} \right)^{2} - \left( \frac{A_{o}}{A_{d}} \right)^{2}}}} & (19)\end{matrix}$

If nothing else, (19) does explain the coinciding of C_(d) and

$\frac{A_{c}}{A_{o}}$values for small

$\frac{A_{o}}{A_{d}}.$Setting

$\frac{A_{o}}{A_{d}} = 0$gives

${C_{d}(0)} = {\sqrt{\frac{1}{\frac{A_{o}}{A_{c}}(0)^{2}}} = {\frac{A_{c}}{A_{o}}{(0).}}}$They are in fact identical.

It's far from obvious from the appearance of (19) that C_(d) would benearly independent of

$\frac{A_{o}}{A_{d}}.$Some words of explanation are in order. Assuming

$\frac{A_{o}}{A_{c}}$smooth, and noting A_(o)=A_(d) means no orifice plate, so A_(c)=A_(d), aremovable singularity at

$\frac{A_{o}}{A_{d}} = 1$becomes apparent:

${C_{d}(1)} = \sqrt{\frac{0}{0}}$before

$1 - \frac{A_{o}}{A_{d}}$is factored out of numerator and denominator. Inserting Weisbach'scorrelation into (19) gives:

$\begin{matrix}{C_{d} = {\sqrt{\frac{1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}}{\left( {{.62} + {{.38}\left( \frac{A_{o}}{A_{d}} \right)^{2}}} \right)^{- 2} - \left( \frac{A_{o}}{A_{d}} \right)^{2}}} = {{\left( {{.62} + {{.38}\left( \frac{A_{o}}{A_{d}} \right)^{3}}} \right)\sqrt{\frac{1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}}{1 - {\left( {{.62} + {{.38}\left( \frac{A_{o}}{A_{d}} \right)^{2}}} \right)^{- 2}\left( \frac{A_{o}}{A_{d}} \right)^{2}}}}} = \left( {{.62} + {{.38}\left( {\left( \frac{A_{o}}{A_{d}} \right)^{3}\sqrt{\frac{1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}}{1 - \left( {{{.62}\left( \frac{A_{o}}{A_{d}} \right)} + {3.8\left( \frac{A_{o}}{A_{d}} \right)^{4}}} \right)^{2}}}} \right.}} \right.}}} & (20)\end{matrix}$

The denominator is an 8^(th) degree polynomial which vanishes at

$\frac{A_{o}}{A_{d}} = 1.$

$1 - {\frac{A_{o}}{A_{d}}\left( {{{but}\mspace{14mu}{not}\mspace{14mu} 1} - \left( \frac{A_{o}}{A_{d}} \right)^{2}} \right)}$can be factored out of numerator and denominator, leaving

$1 + \left( \frac{A_{o}}{A_{d}} \right)$divided by an exceedingly cumbersome seventh degree polynomial. (20)sags slightly from 0.62 at

$\frac{A_{o}}{A_{d}} = 0$to 0.61 at 0.4 then works its way up to over 0.68 at 1. Since C_(d) isconsidered a slowly and steadily increasing fraction of

$\frac{A_{o}}{A_{d}},$this would seem to eliminate Weisbach's expression for

$\frac{A_{c}}{A_{o}},$although it does demonstrate weak dependence of C_(d) on

$\frac{A_{o}}{A_{d}}.$Looking again at (19), note that if

$\frac{A_{o}}{A_{c}}$were a polynomial in

$\left( \frac{A_{o}}{A_{d}} \right)^{2},$equal to 1 at

${\frac{A_{o}}{A_{d}} = 1},$then

$1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}$would necessarily factor out of

$\left( \frac{A_{o}}{A_{c}} \right)^{2} - {\left( \frac{A_{o}}{A_{d}} \right)^{2}.}$The unique 1^(st) degree polynomial in

$\left( \frac{A_{o}}{A_{d}} \right)^{2}$satisfying these requirements and

${{\frac{A_{c}}{A_{o}}(0)} = c};$e.g. c=0.62 (Weisbach), c=0.611 (Kirchoff 1869: infinite slot; 2-dconformal mapping), is

$\begin{matrix}{{\frac{1}{c} - {\left( {\frac{1}{c} - 1} \right)\left( \frac{A_{o}}{A_{d}} \right)^{2}}},{{{or}\mspace{14mu}\frac{A_{c}}{A_{o}}} = \frac{c}{1 - {\left( {1 - c} \right)\left( \frac{A_{o}}{A_{d}} \right)^{2}}}}} & (21)\end{matrix}$

With c=0.611 (Kirchoff 1869),

${A_{c}\text{/}A_{o}} = \frac{.611}{1 - {{.389}\mspace{11mu}\left( \frac{A_{o}}{A_{d}} \right)^{2}}}$lies very close to Weisbach's

${.62} + {{.38}\mspace{11mu}\left( \frac{A_{o}}{A_{d}} \right)^{3}}$in fact the c=0.60 and c=0.62 curves tightly bracket Weisbach's, lendingsupport to the new correlation (21) with Kirchoff's 0.611. (21) is nomore complex than Weisbach's (11) and will prove advantageous in whatfollows.

Substitution of (21) into (19) gives, far from the cumbersome (20)resulting from insertion of Weisbach's correlation, a simple resultstanding in clear relation to (21):

$\begin{matrix}{C_{d} = \frac{c}{\sqrt{1 - {\left( {1 - c} \right)^{2}\left( \frac{A_{o}}{A_{d}} \right)^{2}}}}} & (22)\end{matrix}$

The square on the (1−c) factor: ((1−0.611)²=0.1513), together with thesquare root (√{square root over (1−0.1513)}≈0.917), combine to creategently increasing curves compared to the superficially strikinglysimilar (21); increasing only about 9% at 1.

The theoretical (17) and the intensely practical US standard (18) havebeen shown to be compatible after all. A link has been forged. In theprocess, two new useful correlations have been adduced:

$\begin{matrix}{\frac{A_{c}}{A_{o}} = {\frac{c}{1 - {\left( {1 - c} \right)\left( \frac{A_{o}}{A_{d}} \right)^{2}}}\mspace{14mu}{and}}} & (21) \\{{C_{d} = \frac{c}{\sqrt{1 - {\left( {1 - c} \right)^{2}\left( \frac{A_{o}}{A_{d}} \right)^{2}}}}},{c \sim {.611}},} & (22)\end{matrix}$

which greatly facilitate modeling of the LFFC.

-   -   Notes: 1.

$\left( \frac{A_{o}}{A_{d}} \right)^{2} = \beta^{4}$

-   -    in terminology familiar to many.        -   2. The

$\sqrt{\frac{2}{\rho}}$

-   -   -    factor appearing in (17) and (18) evaluates to about            -   4000-4005 f.p.m/√(in. wg.) in English units.

IVB The Orifice Plate Coefficient

There appears to be no standard usage for the terms flow coefficient anddischarge coefficient. Here, “discharge coefficient” is used only inconnection with (18), in the combination

$\frac{C_{d}}{\sqrt{1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}}}$to form the more general C_(F). Flow coefficient, then, is the generalterm applied to the coefficient C_(F) in (16),

$\frac{C_{d}}{\sqrt{1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}}}$being available as a replacement in cases in which C_(F) blows up for

$\left. \frac{A_{o}}{A_{d}}\rightarrow 1. \right.$

C_(F) does blow up, and is often replaced by

$\frac{c_{d}}{1 - \left( \frac{A_{o}}{A_{d}} \right)^{2}},$particularly in the US, in the standard tap setup

in FIG. 4. The static pressure becomes the same upstream and downstreamas

$\left. \frac{A_{o}}{A_{d}}\rightarrow 1 \right.$and the plate disappears, so the above denominator does→0.

If

$\frac{A_{o}}{A_{d}}$is not ≈1, and the upstream face of the orifice plate meets the ductwall cleanly at 90°

,that corner is a stagnation point (circle, really). v=0 right there, soTP=SP and a sufficiently small tap at that point will read TP. Or, aPitot tube can be used in the undisturbed upstream flow. Either way,there results

$\begin{matrix}{{{{\Delta\; P} = {{{TP} - \left( {{TP} - {\rho\frac{v_{c}^{2}}{2}}} \right)} = {{\rho\frac{v_{c}^{2}}{2}} = {\frac{\rho}{2}\left( \frac{Q}{A_{c}} \right)^{2}}}}},{so}}{Q = {{A_{c}\sqrt{\frac{2\;\Delta\; P}{\rho}}} = {\left( \frac{A_{c}}{A_{o}} \right)A_{o}\sqrt{\frac{2\;\Delta\; P}{\rho}}}}}} & \left( {23a} \right)\end{matrix}$

Compare (16):

$\begin{matrix}{C_{F} = {\frac{A_{c}}{A_{o}}.}} & \left( {23b} \right)\end{matrix}$

The contraction coefficient, which required so many pages indevelopment, is the flow coefficient. Not only does C_(F) not blow up;it never exceeds 1. With amplifying downstream tap, the maximum dropseven lower (higher magnification).

This is the preferred implementation: upstream TP tap, so

${C_{F} = {\frac{A_{c}}{A_{o}} = \frac{c}{1 - {\left( {1 - c} \right)\left( \frac{A_{o}}{A_{d}} \right)^{2}}}}},{c\text{∼}{.61}},\frac{A_{o}}{A_{d}}$as described in the next section. When static upstream taps aremandated, the new correlation (22) can be used with (18), or (21) with(17).

When Pitot tubes are ruled out; in particular if the fluid containsparticulates which would eventually block a pitot tube, one need notresort to static upstream taps. An orifice ring: an orifice plate with

${\frac{A_{o}}{A_{d}}\text{∼}{.8}\mspace{14mu}{or}\mspace{14mu}{.9}},$installed upstream of the LFFC, affords an upstream stagnation circlefrom which TP may be tapped.

The Butterfly Damper

Referring to FIGS. 18G to 18I, the butterfly damper can be viewed as avariable orifice plate with projected open areaA_(o)=A_(duct)−A_(damper)*cos(θ). Positive seal is possible using anannular seat, either very precisely machined or with a gasket working incompression (7 c). In some realizations the latter is implemented.Because of variable gasket relaxation and memory set, and the complexityof flow through the nearly closed damper, the first few degrees ofopening do not give reliable differential pressure readings in such animplementation.

The 2-stage Flow Station/Damper

The 2-stage damper overcomes the limitations of the standard butterflydamper as a flow measuring device. The Vena Contracta of the inner diskis controlled, not by the area projected normal to the duct as in thesimple butterfly damper, but by the projection of the inner annulusopening A_(o) normal to the faces of the annulus and opening diskitself. See FIGS. 18J and 18K.

A_(o)=A_(disk) sin θ (not cosine, as with the outer damper). The diskand annulus (possibly overlapping) opening sequence satisfiesA _(o) ≈A _(duct) sin θ_(disk)+(A _(duct) −A _(disk))(1−cos θ_(annulus))

As shown in FIG. 18L with the annulus, the first few degrees of diskopening are concerned with initial gasket decompression. After that, adelayed sin(θ−θ_(o)) curve sets in. Gasket set and relaxation do notsubstantially affect this curve, which is controlled by flow along thedisk face and annulus face (7 d). This picture is complicated by thefact that full gasket decompression does not occur simultaneously at allpoints around the disk. The point farthest from the shaft may decompressfully at 2°, say; then the opening appears in the shape of a wideningsmile as the disk opens. This actually affects the curve (7 f) verylittle, but accounting for it greatly complicates the appearance of theflow coefficient formula.

At 100% open, the open area is not quite A_(duct). The shaft and, ifused, annular wall gasket remain as obstructions in an otherwise clearflow field. These account for nearly the entire pressure drop at 100%open, so must be modeled carefully in the formula. Formula elements arelisted in the appendix. These are assembled in accord with theimplementation to give the appropriate flow coefficient as function of %open. In preferred implementations, readings are obtained from a TPsensor upstream of the damper and a downstream SP tap in specifiedamplifying locations tight to the back of the annulus, slightlydepressing the curve (7 f). Lower flow coefficient represents highermagnification, of course. Since between say 2% and 10% the flowcoefficient increases linearly from 0 (if no leakage), maximummagnification is theoretically infinite, subject to practicalconsiderations of actuator consistency at setting and defining angularposition etc.

Reduction to Practice

Although, theoretical representations such as the above are extremelyuseful in working out new designs, actual measurements made on physicalmodels must always take precedence. A table of measured flowcoefficients vs % open rather than the theoretical formula will beprovided for each LFFC-based product and configuration, basedparticularly on the upstream sensor being used. If an actuator withsignificant hysteresis is mandated, no single table can be used unlessthe hysteresis is uniform and predictable, so that actual damperposition can be inferred from readings. Inexpensive actuators withoutsignificant hysteresis are readily available.

Measurement at Very Low Reynolds Numbers

With the exception of the remarkable Moody Chart, all commonly used flowand fitting loss coefficient values are valid only at sufficiently highReynold Numbers. An auxiliary table may be incorporated into LFFCproduct configurations to indicate the boundary of theReynolds-independent regime in which the Flow Coefficient depends onlyon damper position. Control extends perfectly well through thelow-Reynolds regime: only display accuracy is affected. Depending onconfiguration of the upstream sensor and the % open of the LFFC, thetransition may be anticipated in the neighborhood of Re≈2000.

In applications where accurate readout is required into this very lowflow regime, a (much larger) low flow coefficient table dependent notonly on damper setting, but on the low Reynolds number as well, providesthis extension.

Actuation

A pair of ganged actuators has been employed, driving concentric shafts,although it's certainly possible to use isolated actuators at each endof collinear damper shafts. A more economical single actuator with2-stage concentric output has been developed.

Installation Requirements

No flow sensing device is able to give an accurate measure of total flowin the presence of a severely disturbed flow profile. Manufacturersrecommend, but seldom get, about 5 diameters of straight duct upstreamof a sensor. For tight installations calibrated profile-preservingelbows may be provided for installation immediately upstream of thesensor/damper.

Legacy VAV boxes require ˜2500 FPM or more maximum entry velocity inorder to achieve turndowns of even 3 or 4. Since downstream devicesrequire at most 700 FPM, this high velocity air is then dumped,requiring extensive silencing to reduce the familiar rumble issuing fromthe ceiling. The LFFC has more than 40:1 turndown from 1200 FPM, usingan ordinary 1″ w.g. transducer. To take full advantage of the more than4:1 energy savings and 20 dB. noise reduction inherent in this designthe final splits in the upstream duct work should be designed to deliver1200 FPM full flow, not 2500 to 3000 FPM, to the LFFC at the end of therun.

Economical transducers are very sensitive to environmental temperature.If the low flow capabilities of the sensor/damper are to be fullyrealized, automatic means must be provided to periodically tie thetransducer inputs together to a common source and update zero-offset.Our complete low flow assemblies include such capability.

System Control

To take full advantage of the energy savings and terminal (as well ascentral) noise reduction made possible by the LFFC, system flow controlshould be based on 1) keeping the all LFFC's satisfied with 2) at leastone LFFC reporting wide open status. This last requirement is essential;otherwise flow control is not well defined: fans might run wide openforcing LFFC's nearly closed, with great noise production and waste ofenergy. Systems controlled as indicated are self-commissioning.

Flow Coefficient Elements

A. Annulus opening Characteristic

-   -   Butterfly dampers are not commonly made with diameter exactly        equal to duct diameter. Extreme accuracy and rigidity is        required to prevent such an arrangement from jamming on the one        hand or leaking on the other. The situation appears to ease        somewhat under slight elliptical elongation of the damper, so it        closes a degree of two shy of perpendicular to the duct. The        above-mentioned difficulties still apply, however and this        easement is seldom seen.        -   (i) One practical arrangement employs dampers with diameter            slightly larger than duct diameter, but with the outermost            few percent made of a flexible gasket material that bends            and or compresses to seal against the duct surface.    -   A simple projected area formula of the form        A _(damper)=MAX(A _(duct) −A _(damper) cos θ_(damper),0)  (25)    -    gives excellent agreement with experiment.        -   (ii) An annular duct-mounted gasket working purely in            compression removes concerns that gasket abrasion and set            may eventually compromise damper seal in arrangements like            (i). The flow picture is greatly complicated by flow            squeezing between the opening damper and just-cleared            gasket. The effect is essentially negligible in the 2-stage            damper, where the outer damper initial opening area is            denominated by the wide open (or nearly so, depending on            possible staging overlap) inner disc.        -   For completeness, development of the controlling formula is            outlined.        -   Referring to FIGS. 18M and 18N, the gasket is compressed            when φ=0, and expands with the damper until it reaches its            uncompressed extension and open are begins to appear,            starting at plane angle

$\psi = {\frac{\pi}{2}.}$

-   -   -    (FIG. 8,9) At general angle ψ the normal from point            P_(gasket)=(r_(g) cos ψ, r_(g) sin ψ, ϵ) (in Cartesian            coordinates) to the point P_(damper)=(r_(g) cos ψ, cos            φ(r_(g) sin ψ+ϵ sin φ, sin φ(r_(g) sin ψ+ϵ sin φ)) has            length δ=r_(g) sin ψ sin φ−ϵ cos φ. The gasket opening area            differential is

${{dA}_{g} = {{\delta{{\frac{d}{d\;\psi}\left( \frac{P_{damper} + P_{gasket}}{2} \right)}}d\;\psi} = {\left( {{r_{g}\sin\;\psi\;\sin\;\varphi} - {ɛ\;\cos\;\varphi}} \right)*r_{g}\sqrt{1 - {\frac{3}{4}\cos^{2}\psi\;\sin^{2}\varphi}}d\;\psi}}},$

-   -   -    which separates into a term that integrates readily and an            elliptic integral of the second kind, which must be suitably            approximated. dA_(g) is the differential area of flow            squeezing through narrow space between the annular gasket            and plate: where the damper is farther from the gasket than            the duct wall the differential form of (22) applies:

$\begin{matrix}{{dA}_{w} = {{\frac{\int_{r_{a}}^{r_{d}}}{\sqrt{1 + {\sin^{2}\psi\;\tan^{2}\psi}}}\mspace{11mu}{rdrd}\;\psi} = {\frac{1}{2}\left( {r_{d}^{2} - \frac{r_{a}^{2}}{1 + {\sin^{2}\psi\;\tan^{2}\psi}}} \right)d\;\psi}}} & (26)\end{matrix}$

-   -   -   At the crossover point dA_(g)=dA_(w), sin(ψ) satisfies a            fourth degree algebraic equation, which, for sufficiently            large φ, has two positive roots. Call the smaller of these,            when they exist, ψ₁. Otherwise

$\psi_{1} = {\frac{\pi}{2}.}$

-   -   -    The annulus open area is then

$\begin{matrix}{A_{annulus} = {{4{\int_{\psi_{o}}^{\psi_{1}}{dA}_{g}}} + {4{\int_{\psi_{1}}^{\frac{\pi}{2}}{{dA}_{w}.}}}}} & (27)\end{matrix}$

$\psi_{o} = {A\;{\sin\left( \frac{ɛ}{r_{g}\tan\;\varphi} \right)}}$

-   -   -    is the angle at which, for given damper opening angle φ,            the damper just clears the gasket. Nothing happens until

${{\geq \varphi_{o}} = {{atan}\left( \frac{ɛ}{r_{g}} \right)}},$

-   -   -    the damper angle at which the tip

$\left( {\psi = \frac{\pi}{2}} \right)$

-   -   -    of the annulus just clears the gasket. The opening sequence            is:

$A = {{0\text{:}\mspace{20mu}\psi_{o}} = {\psi_{1} = \frac{\pi}{2}}}$

-   -   -    until φ≥φ≈2.2°, ≈1.24% of the full 2 stage sequence, and            ψ_(o) drops below

$\frac{\pi}{2}.$

-   -   -    At around 3°, 1.7% of range, ψ₁ drops below

$\frac{\pi}{2}.$

-   -   -    ψ₁ and ψ_(o)→0 as

$\left. \varphi\rightarrow{\frac{\pi}{2}.} \right.$

-   -   -    The annular gaskets end at around ψ=4°, where they meet the            damper bushings at the duct wall. The bushings together with            the shaft between act as small obstruction, not limiting the            effective area of opening but providing a small contribution            to the wide open damper ΔP. Letting ψ₁ and ψ_(o)→0 allows            these losses to be treated separately from the orifice plate            opening characteristic.        -   A similar analysis applies to rectangular and other convex            duct and damper shapes.

B. Disk Opening Characteristic: 2 Stage Damper

-   -   Referring to FIGS. 18O and 18P, the inner damper element        slightly overlaps the generally central opening in the outer        damper element. The opening is here treated as circular and the        slightly larger inner damper element as a modified disk: a        similar analysis applies to elliptical and other convex element        and opening shapes. The overlap region is provided with        compressible gasket material, embedded in either or both the        annulus and disk. The normal distance from the point        P_(ann)=(x,y,s), x²+y²=r², on the opening near edge to the disk        surface is δ=y sin θ−s cos θ−t, with θ the disk opening angle        relative to the annulus, s half the annulus thickness, and t        half the disk thickness. The projected opening area is

$\begin{matrix}{{A_{disk} = {{4{\int_{0}^{r_{0}}{{{MAX}\left( {\delta,0} \right)}{dx}}}} = {{4{\int_{0}^{r_{0}}{{{MAX}\left( {{{\sqrt{r^{2} - x^{2}}\sin\;\theta} - {s\;\cos\;\theta} - t},0} \right)}{dx}}}} = {2\left\lbrack {{r^{2}a\;{\sin\left( \frac{x_{o}}{r} \right)}} - {x_{o}\left( {{s\;\cos\;\theta} + t} \right)}} \right\rbrack}}}},} & (28) \\\left. \mspace{79mu}{{{{with}\mspace{14mu} x_{o}} = \sqrt{{MAX}\left( {r^{2} - \left( \frac{{s\;\cos\;\theta} + t}{\sin\;\theta} \right)^{2}} \right.}},0} \right) & \;\end{matrix}$

-   -   The disk clears the gasket for x<x_(o). x_(o)>0 when θ>θ_(o),        the angle at which the tip of the disk just clears the gasket.        θ_(o) satisfies r sin θ_(o)=s cos θ_(o)+t. If t<<s, this becomes

${\theta_{o} = {{atn}\frac{s}{r}}};$

-   -    if s<<t,

$\theta_{o} = {a\;\sin{\frac{t}{r}.}}$

-   -   The open area of the 2-stage flow station/damper is then        A _(o) =A _(disk) +A _(annulus).  (29)    -   The device functions as a variable area orifice plate almost        over its entire range. Until the device is almost 100% open, a        common pool of essentially still air in the shadow of the damper        unites the venae contractae of flows emerging from (in this        case) up to four separate areas of varying shape and        orientation, so that various areas are simply added together, as        was done in (29), to produce A_(o) for use in the correlation

$\begin{matrix}{C_{F} = {\frac{A_{c}}{A_{o}} = \frac{c}{1 - {\left( {1 - c} \right)\left( \frac{A_{o}}{A_{d}} \right)^{2}}}}} & {{Eq}.\mspace{14mu}(21)}\end{matrix}$

-   -    with A_(d) the total duct area.    -   c=0.611 gives Kirchoff's 1869 result asymptotically.

C. Residual Effects at 100% open

-   -   At 100% open, there is no orifice plate, and C_(F) is nearly 1,        assuming the upstream tap reads TP. The downstream tap, out of        the airstream tucked in behind, possibly integral with the        damper shaft, reads a little lower than surrounding SP because        the flow is moving slightly faster around the obstructing shaft,        and SP+VP is conserved. This effect is lumped together with        residual pressure drops due to the upstream sensor, wall        friction, and annular gasket (if employed) into a constant        C_(o), and replace (23a) by

$\begin{matrix}{{{\Delta\; P} = {{{TP} - \left( {{TP} - {\frac{\rho}{2}\left( \frac{Q}{A_{c}} \right)^{2}} - {{Co}\frac{\rho}{2}\left( \frac{Q}{A_{d}} \right)^{2}}} \right)} = {\rho\frac{Q^{2}}{2}\left( {\frac{1}{A_{c}^{2}} + \frac{Co}{A_{d}^{2}}} \right)}}},{or}} & \left( {30a} \right) \\{\mspace{79mu}{Q = \frac{A_{o}\sqrt{\frac{2\;\Delta\;\rho}{\rho}}}{\sqrt{\left( \frac{A_{o}}{A_{c}} \right)^{2} + {{Co}\left( \frac{A_{o}}{A_{d}} \right)}^{2}}}}} & \left( {30b} \right)\end{matrix}$

-   -   so C_(F) becomes

$\begin{matrix}\frac{\frac{A_{c}}{A_{o}}}{\sqrt{1 + {{{Co}\left( \frac{A_{c}}{A_{o}} \right)}^{2}\left( \frac{A_{o}}{A_{d}} \right)^{2}}}} & \left( {30c} \right)\end{matrix}$

-   -   C_(o) is measured individually in each configuration for        incorporation into (30c). This, with the new correlation

${\frac{A_{c}}{A_{o}} = {\frac{c}{1 - {\left( {1 - c} \right)\frac{A_{o}}{A_{d}}}}\mspace{14mu}(21)\mspace{14mu}\left( {c\text{∼}{.61}} \right)}},{{and}\mspace{14mu}\frac{A_{c}}{A_{d}}\mspace{14mu}{from}\mspace{14mu}(29)},$

-   -    comprises the theoretical foundation for the Low Flow Fluid        Controller.

The methods, systems, and devices discussed herein are examples. Inparticular the indicated temperature and timing values as well assignaling protocols are to be taken as examples. Various configurationsmay omit, substitute, or add various method steps or procedures, orsystem components as appropriate. For instance, in alternativeconfigurations, the methods may be performed in an order different fromthat described, and/or various stages may be added, omitted, and/orcombined. Also, features described with respect to certainconfigurations may be combined in various other configurations.Different aspects and elements of the configurations may be combined ina similar manner. Also, technology evolves and, thus, many of theelements are examples and do not limit the scope of the disclosure orclaims.

Specific details are given in the description to provide a thoroughunderstanding of example configurations (including implementations).However, configurations may be practiced without these specific details.For example, well-known circuits, processes, algorithms, structures, andtechniques have been shown without unnecessary detail in order to avoidobscuring the configurations. This description provides exampleconfigurations only, and does not limit the scope, applicability, orconfigurations of the claims. Rather, the preceding description of theconfigurations will provide those of skill with an enabling descriptionfor implementing described techniques. Various changes may be made inthe function and arrangement of elements without departing from thespirit or scope of the disclosure.

Also, configurations may be described as a process which is depicted asa flow diagram or block diagram. Although each may describe theoperations as a sequential process, many of the operations may beperformed in parallel or concurrently. In addition, the order of theoperations may be rearranged. A process may have additional steps notincluded in the figure. Furthermore, examples of the methods may beimplemented by hardware, software, firmware, middleware, microcode,hardware description languages, or any combination thereof. Whenimplemented in software, firmware, middleware, or microcode, the programcode or code segments to perform the necessary tasks may be stored in anon-transitory computer-readable medium such as a storage medium.Processors may perform the described tasks.

Furthermore, the example embodiments described herein may be implementedas logical operations in a computing device in a networked computingsystem environment. The logical operations may be implemented as: (i) asequence of computer implemented instructions, steps, or program modulesrunning on a computing device; and (ii) interconnected logic or hardwaremodules running within a computing device.

Any of the modules or components of system 1200, or any combinations ofsuch modules or components, can be coupled with, or integrated into, orotherwise configured to be in connectivity with, any of the fluid flowcontrol embodiments disclosed herein. Relatedly, any of the hardware andsoftware components discussed herein can be integrated with orconfigured to interface with other flow control systems used in a singlelocation or across multiple locations.

Each of the calculations or operations described herein may be performedusing a computer or other processor having hardware, software, and/orfirmware. The various method steps may be performed by modules, and themodules may comprise any of a wide variety of digital and/or analog dataprocessing hardware and/or software arranged to perform the method stepsdescribed herein. The modules optionally comprising data processinghardware adapted to perform one or more of these steps by havingappropriate machine programming code associated therewith, the modulesfor two or more steps (or portions of two or more steps) beingintegrated into a single processor board or separated into differentprocessor boards in any of a wide variety of integrated and/ordistributed processing architectures. These methods and systems willoften employ a tangible media embodying machine-readable code withinstructions for performing the method steps described above. Suitabletangible media may comprise a memory (including a volatile memory and/ora non-volatile memory), a storage media (such as a magnetic recording ona floppy disk, a hard disk, a tape, or the like; on an optical memorysuch as a CD, a CD-R/W, a CD-ROM, a DVD, or the like; or any otherdigital or analog storage media), or the like.

Referring to FIGS. 13A-D, another embodiment of a damper assembly 1300is illustrated. Damper assembly 1300 is adapted to be positioned withina fluid flow pathway of a duct and functions as an orifice plate thatdefines a variable opening for receiving various types of fluid andcontrol fluid flow there through. Damper assembly 1300 comprises a frame1302 having a right edge 1304, left edge 1306, lower edge 1308, andupper edge 1310. Frame 1302 defines a central opening 1312 within whicha plurality of blades 1314 a-1314 h are disposed in a generally parallelorientation relative to each other. Each of blades 1314 a-1314 h ispivotable along its longitudinal axis on corresponding shafts 1316a-1316 h, as shown in FIG. 13D with shafts 1316 a-1316 h extending fromright edge 1304 to left edge 1306 of frame 1302. Shafts 1316 a-1316 hneed not be a continuous single component as long as blades 1314 a-1314h are pivotable along its longitudinal axis. Each of shafts 1316 a-1316h is attached to corresponding gears 1318 a-1318 h, and the rotation ofeach gear is controlled by actuators 1320 a-1320 d. In this embodiment,there are four actuators (1320 a, 1320 b, 1320 c, 1320 d), and it can beseen that each actuator rotates a pair of gears; for example, actuator1320 a rotates gears 1318 a and 1318 b, actuator 1320 b rotates gears1318 c and 1318 d, actuator 1320 c rotates gears 1318 e and 1318 f, andactuator 1320 d rotates gears 1318 g and 1318 h. Turning to FIG. 13C,when actuator 1320 a acts upon gears 1318 a and 1318 b, gear 1318 a willrotate in a direction opposite to the direction that gear 1318 brotates. The rotation of gear 1318 a will open corresponding blade 1314a, and similarly, the rotation of gear 1318 b will open correspondingblade 1314 b. Blades 1314 a and 1314 b may be larger than blades 1314 cand 1314 d whereby a larger area of central opening 1312 would becovered by blades 1314 a and 1314 b than by blades 1314 c and 1314 d.The variation in blade sizing provides for the benefit of increased“fine-tuning” of flow selection between the range of minimum and maximumflow rates. The optimum sizing of blades 1314 a-1314 h are determined byflow rate requirements and space considerations.

Referring to FIG. 14, another embodiment of damper assembly 1400 isgenerally shown. Damper assembly 1400 in this embodiment has twoactuators 1420 a and 1420 b to vary the position of blades 1414 a-1414h. Connecting gear 1422 a articulates gears 1418 a and 1418 b whileconnecting gear 1422 b articulates gears 1418 b and 1418 c. As such,when actuator 1420 a rotates gears 1418 c and 1418 d, gears 1418 a and1418 b are correspondingly rotated by the articulation of connectinggears 1422 a and 1422 b respectively. Similarly, connecting gear 1422 darticulates gears 1418 h and 1418 g while connecting gear 1422 carticulates gears 1418 g and 1418 f. As such, when actuator 1420 brotates gears 1418 e and 1418 f, gears 1418 g and 1418 h arecorrespondingly rotated by the articulation of connecting gears 1422 cand 1422 d respectively. In this embodiment, it can be seen that eachactuator rotates four gears; for example, actuator 1420 a rotates gears1418 a, 1418 b, 1418 c, and 1418 d; and actuator 1420 b rotates gears1418 e, 1418 f, 1418 g, and 1418 h. Actuator 1420 a and actuator 1420 bmay operate independently of each other to provide the flow throughdamper assembly 144 as required, such as for example, in sequence.Blades 1414 a and 1414 b may be larger than blades 1414 c and 1414 dwhereby a larger area of central opening 1412 would be covered by blades1414 a and 1414 b than by blades 1414 c and 1414 d. The variation inblade sizing provides for the benefit of increased “fine-tuning” of flowselection between the range of minimum and maximum flow rates. Theoptimum sizing of blades 1414 a-1414 h are determined by flow raterequirements and space considerations. Typically, the low-flow blade isall or part of the middle blade if there are an odd number of blades indamper. If there are an even number of blades in damper, as shown inFIGS. 16, 15, and 13A, the low-flow blade is typically located justbelow the middle section of the damper assembly, particularly in outsideair service. In exhaust or relief air service, it may be just above themiddle. In these services the low edge of the blades is naturally to theoutside. In a 6 or 7 identical blade damper assembly (not shown), one ofthe blades may for example be split proportionally into three-quartersand one-fourths, with the low-flow section comprising the three-quartersportion of the split blade and the remaining one-forth portion of thesplit blade driven together along with the remaining blades thatcomprise the high-flow blades. The actuators could be ganged, side byside, or on opposite ends of the damper. In 4-blade to 7-blade damperassemblies, one blade may have two independent sections, as illustratedin FIGS. 16A and 16B for a 4-blade damper assembly, and locating thelow-flow actuator on the opposite side of the damper assembly issimplest. In 9 or more blade assemblies, 2 or more blades or fractionsof blades may be ganged to comprise the low-flow section of the damper.Alternatively, with the split blade, nesting shafts may be used whereina rod driven by the low-flow actuator inside a tube ganged with theother remaining blades. Side-by-side actuators make for a more robustand compact arrangement of a damper assembly. In all cases, thepreferred ratio of low-flow to total area is approximately 1:8. Analternative to splitting blades is providing a complete low flow bladeof height ⅛ of the total height of the damper, different from the otherblades except in the special case of 8 blades total: FIG. 15. If thetotal number of blades is n, the low-flow blade would have height˜(n−1)/7 of the others, adjusted for blade overlap. This would work wellwith more than 8 blades total, so the low-flow blade would be higherthan the others, but below about n=6, the low-flow blade would become soskinny performance would begin to suffer.

While the various embodiments of the damper assembly disclose aplurality of actuators for blade positional control, it is alsocontemplated that a damper assembly may comprise a single actuatorcapable of staging a low-flow and high-flow actuation of bladepositioning using a progressive linkage system, gearing system, or camrace (not shown). Moreover, while the various embodiments disclose aplurality of horizontally disposed blades of the damper assembly, it isalso contemplated that the damper assembly may comprise a plurality ofvertically disposed blades. Nevertheless, blades are disposed in agenerally parallel orientation relative to each other. A single actuatordamper assembly progressively stages the low flow and high flowactuation of blade positioning by a linkage, gearing, or cam system,wherein the opening of the low flow blade(s) and high flow blades areschematically illustrated in FIG. 4B. For example, at the 0% position,low flow blade 1615 and high flow blades 1614 a, 1614 b, 1614 c, 1614 dare completely closed thereby blocking airflow there through. Low flowblade 1615 opens progressively between the 0% to 50% position of gear160 with low flow blade completely open at the 50% position. High flowblades 1614 a, 1614 b, 1614 c, 1614 d open progressively between the 50%to 100% position with the high flow blades 1614 a, 1614 b, 1614 c, 1614d completely open at the 100% position. It can be seen that at the 100%position, all the blades are completely open, thereby allowing maximumairflow there through, and that the reverse process occurs for closingthe blades.

Damper assembly may be housed or un-housed in a tube or other geometrichousing defining a portion of the flow pathway as shown in FIG. 12.Fluid flow measurements through initial opening 1615 can be done withpressure sensor P₂ in front of damper assembly and pressure sensor P₁behind damper assembly. In a preferred implementation, openings facingupstream in an upstream sensor tube may be located somewhat toward theboundary between the low-flow opening and high flow area, to delaytransition into the low Reynolds flow regime. Downstream pressures maybe measured in the wake of a high-flow shaft or section of shaft; or inthe blade damper case, by a simple pressure tap: out of the airstream ineither case. Alternatively, pitot tubes, orifice rings (in the ductedcase), and the like may be used to measure fluid flow through damperassembly. From a fully closed position, the preferred opening sequenceis to first open the low flow region, followed, possibly with someoverlap, by opening the high flow region. Flow rates between the minimumand maximum may be obtained by opening the blades in preferred order.Blades may be of identical sizes or of different sizes relative to eachother. A variable speed fan (not shown) is disposed up- or down-streamof the damper assembly to generate the fluid flow through the flowpathway and through the damper assembly.

Damper assemblies as described herein allow for more effective zoningand flow control since damper assemblies can not only measure air flowthere through, but also air temperature and CO₂ concentrations of thezone. The sensors that measure zone temperature and CO₂ concentrationsmay communicate with a controller 1200 via wired or wireless signals.Damper assembly can be controlled through the cloud, wi-fi, or a smartdevice, via wireless communication such as wi-fi, Bluetooth, infrared,or the like, due to real time flow measuring capabilities. Smart devicesmay include, and is not limited to smart phones, tablets, universalremote controllers, and the like. Temperature sensors may includecombination temperature sensor learning thermostats, such as the NestLearning Thermostat. The output of flow and/or temperature etc.measurement is sent to controller 1200 in FIG. 12 that provides a signalto control actuators that, in turn, control the position of the bladesin damper assembly. Controller 1200 comprises a processor, a memorycoupled to and readable by the processor. The memory includesinstructions stored therein that determine present flow from a pressuredifferential between the pressure sensors P₁ and P₂ and the position ofthe blades based on positional feedback received from the actuators, andcontinually adjusts a blade or blades position(s) to control flowrate tomaintain required flow, temperature. or maximum allowed CO₂concentrations in the zone. Note that controlling all three at oncerequires communication with the central controller to adjust flow and %outside air. A damper controller signals a fan controller when it iswide open and the desired condition based on room temperatures andmaximum allowed CO₂ content is not being achieved. In such instance, thecentral controller slowly increments fan speed when more flow isrequired; outside and return air dampers if more outside air isrequired, allowing for relaxation time, until no damper controllerreports being beyond its control range, and at least one dampercontroller reports being at the wide open damper limit. The fancontroller adjusts fan speed to maintain that condition. The fan(s)is/are always at the lowest setting such that all zones are satisfiedand at least one damper is wide open unless the fan setting is atmaximum, as for example, on a Monday morning startup. Under suchconditions, an auxiliary algorithm may be employed to instruct anydamper controllers located in non-essential areas to limit flow so thatcritical areas may receive maximum flow until satisfied, after whichthey are allowed to gradually open subject to maintaining satisfactionin the critical areas. Normal mode resumes when the fan is no longer atmaximum. It can thus be seen that such a system is clearlyself-balancing/self-commissioning.

It is contemplated that all the blades may be controlled by a singleactuator, as described earlier, wherein a linkage, cam or gearingassembly operatively and/or mechanically sequences the blades asrequired for generally staged control by the single actuator.Additionally, an uneven combination of actuators and blades may beimplemented, by for example, having one pair of blades controlled by oneactuator and the remaining set of blades controlled by another actuator.Furthermore, while this embodiment shows central opening 1615 asgenerally rectangular, it is contemplated that various openingconfigurations (e.g. circle, triangle, diamond, trapezoid, rectangle,ellipse, semi-circle, and quarter circle) may also be implementedsuccessfully. Those skilled in the art will appreciate that damperassemblies provide for a multi-stage damper flow function that is verycost effective with high turndown ratio design that results in veryaccurate low flow capabilities while still allowing for very high flowrates when required. Those skilled in the art will also appreciate thatdamper assemblies disclosed herein may incorporate any number of bladesthat allow it to meet its overall design objectives. The advantages of amulti-stage damper design include a cost effective way to measure andcontrol flow, use of existing tooling for damper construction andintegration, fewer part numbers associated with high turndown ratios,complete integration of hardware and peripherals into the damperassembly.

Referring to FIGS. 15A and 15B, another embodiment of damper assembly1500 is generally shown. Damper assembly 1500 in this embodimentcomprises eight blades 1514 a, 1514 b, 1514 c, 1514 d, 1514 e, 1514 f,1514 g, 1514 h (1514 a-1514 h) and has two actuators, high-flow actuator1520 a and low-flow actuator 1520 b to vary the position of blades 1514a-1514 h. High-flow actuator 1520 a controls the position of seven ofthe blades, namely blades 1514 a, 1514 b, 1514 c, 1514 d, 1514 f, 1514g, 1514 h. High-flow actuator 1520 a articulates shaft 1515 that in turnarticulates links 1518 a, 1518 b 1518 c, 1518 f, 1518 g, 1518 h that areconnected to blades 1514 a, 1514 b, 1514 c, 1514 f, 1514 g, 1514 h,respectively. High-flow actuator 1520 a may be directly attached toblade 1514 d, or alternatively, control blade 1514 d via a link (notshown). Low-flow actuator 1520 b controls only the position of blade1514 e and may be directly attached to blade 1514 e, or alternatively,control blade 1514 e via a link (not shown). Low-flow actuator 1520 b isnot connected to shaft 1515 and thereby controls blade 1514 findependently of the other seven blades. As the name implies, low-flowactuator 1520 b provides for a low flow rate through damper 1500 bycontrolling and opening only blade 1514 e, as shown in FIG. 15A, whilehigh-flow actuator 1520 a provides for a higher flow rate through damper1500 by controlling and opening the remaining seven blades of damper1500. When a maximum flow rate is required, both high-flow actuator 1520a and low-flow actuator 1520 b opens all the blades 1514 a-1514 h ofdamper 1500. In a 7-blade to 9-blade damper (not shown), the low flowblade may comprise the blade 1514 e in its entirety. More generally, byusing blades of several different widths, say 3″ through 7″, dampers ofany required height may be devised, with low-flow blade openingtypically, but not necessarily, about ⅛ the total damper face area. Thelow-flow blade is generally placed near the middle of the damper, asshown here.

Referring to FIGS. 16A and 16B, another embodiment of the LFFC damperassembly 1600 is generally shown. Damper assembly 1600 in thisembodiment comprises four blades 1614 a, 1614 b, 1614 c, 1614 d and hastwo actuators, high-flow actuator 1620 a and low flow actuator 1620 b.One of the blades 1614 c is split into two separately controlledsections with the low-flow open area generally comprising about ⅛ thetotal damper face area. Even though they share a common pivot axis,blade 1614 c and low-flow blade 1615 operate independently from eachother as low-flow actuator 1620 b controls only low-flow blade 1615.High-flow actuator 1620 a controls high-flow blades 1614 a-1614 d via ashaft 1617 that articulates links 1618 a, 1618 b, 1618 c, 1618 d thatare connected to high-flow blades 1614 a, 1614 b, 1614 c, 1614 d,respectively. High-flow damper 1620 a is preferably positioned on theopposite side of low-flow actuator 1620 b of damper assembly 1600 toprovide for better clearance of shaft 1617 and links 1618 a-1618 d.Low-flow blade 1615 typically opens first followed by the remaining highflow blades 1614 a-1614 d. High flow blades 1614 a-1614 d may beginopening before low-flow blade 1615 is completely open. By appropriatelysplitting (generally) one of many typically identical width blades,dampers of any required height may be obtained.

Referring now to FIGS. 17A and 17B, a reheat box 1700 in accordance withthe present invention is generally shown. Reheat box 1700 includes ahousing 1702 having an inlet end 1704 and an outlet end 1706. A coil1708 is disposed within housing 1702 through which air entering inletend 1704 of housing 1702 flows through to outlet end 1706 as depicted bythe flow direction arrow. Also disposed within housing 1702 is a damperassembly 1710 located downstream of coil 1708. Sensor tubes 1709 a and1709 b are disposed upstream and downstream, respectively, of damperassembly 1710. Damper assembly 1710 may include a nested butterfly type1711 as shown or blade type damper (not shown) controlled by an actuator1712. Damper assembly 1710 regulates the flow of air coming through coil1708 that exits outlet end 1706 of housing 1702. The airflow isstabilized passing through coil 1708 preserving air flow readingaccuracy even when upstream air is extremely non-uniform. Coil 1708 actsas a flow stabilizer thus allowing for a more compact housing 1702.Piping 1714 exiting coil 1708 determines a right-hand (as shown) orleft-hand piping configuration of Reheatbox 1700. Reheat box 1700 allowsfor either a right-hand or left-hand piping configuration by simplyflipping coil 1708 or the entire box by 180 degrees to accommodate anyrequired configuration. This simplifies assembly and integration of VAVbox 1700.

The coil is typically rotated (tipped) relative to the direction ofupstream and downstream airflow to increase flow area and reducepressure drop. FIG. 17B represents a top or bottom view if the coil isrotated about a vertical axis and a side view (except for theorientation of the coil tubes) if the coil is rotated about a horizontalaxis. To keep the unit short, the axis of rotation generally runs thelonger way across the duct, which is usually the width. So the left sideof 17B is generally a side view, except for tube orientation. The dampershaft also usually runs the long way, so 17B does not reflect the usualcombination.

Reheat box 1700 has approximately a 250:1 turndown ratio as it allowsfor air to enter the coil and discharge the tempered air through damperassembly 1710. As such, this allows for lower cost alternative andbetter performance from coil 1708. The damper technology, as disclosedherein, makes possible the next generation in low air volume systems andis applicable to both cooling and heating thermal transfer devices.Moreover, with this damper technology, high turndown noise issues areeliminated, the housing can be extended, and a damper assembly can beconfigured to the exact dimensions of the housing. No internal liner isrequired as unit is insulated externally. Little skew part numbers iscreated and better heat transfer is generated with this design.

Reheat box 1700 represents an improvement over current VAV boxes.Current VAV boxes with coils have the air flowing through an air valveat approximately 3000 fpm into a plenum and transitioning the air downto approximately 1500 fpm before flowing through the coil. These currentVAV boxes have only approximately a 5:1 turndown ratio from 3000 fpm,limited flow measurement accuracy, and undesirable acoustics. Thepresent design supports 40:1 turndown from just 1400 fpm. This lowvelocity capability relieves noise and air pressure drop problems.Current VAV boxes use a round air valve that blows into a square plenumand then across the thermal transfer unit that is typically an electricreheat or a hot water coil. The round inlet is necessary because anairflow velocity of 500 fpm to 3000 fpm through the inlet is required tomeasure the flow and/or pressure. The transducer on the VAV controllercannot accurately measure the flow and/or pressure below 500 fpm to 700fpm, and therefore controlling the zone temperature and airflow isdifficult. As such, the air is pumped into a square plenum where itdischarges at about 750 fpm to minimize noise and to allow for properheat transfer across the hot water coil. Cooling coils cannot be used asthey require 550 fpm or less to operate without creating moisture in theair stream. Air enters through the 5:1 turndown air valve for measuringpurposes and into a plenum and then flows across the coil in a blowthrough configuration, which also causes spotting on the coil. The lowflow damper does not require a high velocity airflow round inlet as on aVAV box. A rectangular Air Valve can be used at the full diameter of lowvelocity rectangular ductwork. Thus, the air can enter through thecoil/thermal transfer unit and discharge out the square air valve box ina draw through configuration. Both heating and cooling coils can be usedas the damper can measure flows down to 10-20 fpm. Coils can beconfigured in various orientations to optimize surface area andperformance parameters economically The low flow damper technology canbe applied to various types of dampers including round, square,rectangular, etc. They can be used in flow control and flow measurementapplications such as air diffusers/vents, air valves, dampers, airhandlers, roof top package units, variable refrigerant systems etc.

Another application for the low flow damper technology is for preventionof infiltration in building and the resulting energy savings therefrom.Virtually all buildings are leaky, which creates no discomfort as longas air is only leaking out and not in. Occupied buildings requireventilation, and the same amount of air must be expelled as is taken in.Infiltration can be prevented if every floor is adequately pressurized,and if the wind-induced pressure were known at every point on thesurface of a building, each floor could be pressurized to slightly abovethe highest outside pressure at that level in order to preventinfiltration. However, since it is not practical to measure the outsidepressure at every point on the surface of a building, wind-inducedpressure at every point on the surface of a building may be approximatedusing only four pressure sensor/transducers by placing one at the centerof each side of a rectangular plan floor and reading inside pressurerelative to outside pressure (ΔP) at that same point. If all fourtransducers read ≥0 differential (inside pressure≥outside pressure), noinfiltration occurs from wind pointing perpendicular to a side of thebuilding. In that case the highest outside pressure (lowest ΔP) is inthe middle of the face right where the pressure reading is taken. As thewind shifts 45 degrees to either side, pointing to a corner of thebuilding, the high pressure point accordingly shifts toward that corner.Using the ΔP's derived from the four pressure transducers, the lowest ΔPanywhere on the floor perimeter can be estimated, as can wind direction.Accordingly, relief dampers can be adjusted to maintain a ΔP≥0 allaround the floor perimeter, eliminating infiltration.

The steps to prevent infiltration into a building floor by use of onlyfour pressure transducers are as follows:

1. Determining Δ_(min) (the lowest of the four measured ΔP's at a givenmoment; Δ₂=2nd lowest ΔP; and Δ_(max)=the highest ΔP, on the sideopposite Δ₂).

2. Calculating x, wherein x=(Δ₂−Δ_(min))/(Δ_(max)−Δ_(min))ϵ[0,1]

3. Applying correction factorK(x)=0.27938343(1−x^(1.8184499))^(2.3339486).(K(x)≈0.2794(1.002−0.1007x−3.0279x²+2.1313x³) is a fair approximation).The corrected Δ=Δ_(min)−K(x)(Δ_(max)−Δ_(min)) estimates the interiorpressure relative to the exterior point of greatest wind impact.

4. Adjusting floor relief dampers to maintain Δ≥0.05 in. w.c. (Whenrelief is via a large central shaft, it is most efficient to allowgreater pressurization on the highest floors in very cold weather;lowest floors in very warm weather, with floor relief dampers wide open.

5. Incrementing damper with smallest flow while Δ>0.05 in. w.c. anddecrement damper with greatest flow while Δ<0.05 in. w.c.

Θ≈45−34.228x+15.001x²−25.784x³ estimates wind direction. Θ=0° indicatesflow □ to the “min” face, and Θ=45° □ indicates flow splitting 50-50 atthe corner where the “min” and “2” faces meet. (Past that halfway point,the “2” and “min” faces switch roles, and the angle decreases back to 0as flow becomes □ to the new “min” face. The previously unlabelled facebecomes the new “max” face)

In legacy designs with large shafts carrying relief and return airtogether to central MER's, control is via the relief/return dampers oneach floor. Controlling both relief and floor pressurization locally andsimultaneously is much more energy efficient and compact than carryingrelief air large distances in large ducts, against up to an inch w.c. ormore stack effect. Four low flow blade dampers per floor are used forlocal relief, preferably in wireless communication with a controllerprovided on one of them, each centered on a building face andcontinuously carry out the building infiltration prevention stepsoutlined above to maintain both floor pressurization and balancedrelief. This process allows 0.05 in. w.c. Pressurization relative to thehighest outside pressure around each floor's perimeter to be maintained.Each low flow blade damper discharges about one-fourth of the totalrequired relief for the floor, less infiltration. The controllercomputes flow through each damper using an algorithm based on AP and theblade opening percentages.

Referring to FIGS. 19A and 19B, an embodiment of the air distributionapparatus 1900 is generally shown. Air distribution apparatus 1900 is adiffuser that comprises a outer troffer plate 1902, an end supply box1904 having at least a pipe 1906 incorporated therein, and a fronttroffer plate 1908. Outer troffer plate 1902, end supply box 1904, andfront troffer plate 1908 together form a housing that defines a plenum1909 space therein. There are a pair of inner troffer plates 1910disposed toward the bottom and within center troffer plate 1912. Innertroffer plates 1910, along with side troffer plates 1912, form airflowpassages that guide and regulate airflow therebetween and out of airdistribution apparatus 1900. Inner troffer plates 1910 have a shapedepending on the radiation pattern of the LED's, and the regulation ofairflow is accomplished by articulating side troffer plates 1912relative to inner troffer plates 1910, whereby side troffer plates 1912are articulable between a closed position and an open position, and anyposition therebetween. The articulation of each side troffer plate 1912may be accomplished by a plurality of hinge plates 1914 that attach eachside troffer plate 1912 to a lever rod 1916. Lever rod 1916 is in turnconnected to a lever rod square 1919 that is articulated by lever joint1920 via lever pin 1922. In one embodiment a linear actuator 1924controls the position of lever joint 1920. It can be seen by thoseskilled in the art that linear actuator 1924 is essentially a motor thatdrives side troffer plates 1912 between a closed position to a fullyopen position and any position therebetween that ultimately adjusts theairflow passage to regulate and control the flow of air from the airdistribution apparatus 1900. A gasket 1938 seals airflow leakage betweeninner troffer plate 1910 and side troffer plate 1912 when the latter isdisposed in a closed position. Although a single linear actuator 1924 isshown, a dual or multiple actuator configuration is also contemplated,and each side troffer plate 1912 may operate independently from theother. Air distribution apparatus 1900 may be scaled to variousdimensions, and it is estimated that a 2 foot×4 foot apparatus with LEDcovers approximately a 100-144 square foot area, or twice that ifsupply-return troffers alternate with return-only troffers. A heat sink1932, typically of aluminum, having a plurality of fins 1933 isincorporated within the plenum that helps remove heat from all thelighting sources thereby greatly reducing energy consumption and greatlyprolonging LED lifetime

Turning to FIG. 19C, the hinge plate 1914 can be seen in greater detail.Hinge plate 1914 incorporates an opening 1926 that receives lever rod1916. Although a generally square profile of opening 1926 is shown,those skilled in the art will appreciate that any profile capable ofreceiving lever rod 1916 will suffice, as long as sufficient friction ismaintained between hinge plate 1914 and lever rod 1916 such that theyremain in a fixed position relative to each other.

Turning to FIG. 19D, lever rod square 1918 can be seen in greaterdetail. Lever rod square 1918 comprises a first opening 1928 at itsdistal end and a second opening 1930 at its proximal end. First opening1928 is adapted to engage lever rod 1916 which in this embodiment has agenerally square profile. Those skilled in the art will appreciate thatany profile capable of engaging lever rod 1916 will suffice, as long assufficient friction is maintained between lever rod square 1918 andlever rod 1916 such that they remain in a fixed position relative toeach other. Second opening 1930 of lever rod square 1918 is adapted topivotably engage with lever joint 1920 and is connected lever pin 1922.

Sensors TP 1934 and SP 1936, as shown in FIGS. 19A, 19B and 19E detectthe surrounding air pressure wherein TP 1934 is located upstream and SP1936 downstream of side troffer plates 1912 of air distributionapparatus 1900. The supply of air enters laterally into air distributionapparatus 1900 and 1940 through pipe 1906 and flows into a plenum spacewithin air distribution apparatus 1900 and 1940. The lateral pipe designallows for a lower profile ceiling space than systems having top mountedsupply pipes. Pressure sensors 1935, 1936, and 1939 provide roompressure and pressure sensors 1934, 1937, and 1938 provide pressuremeasurements within plenum 1909.

Air distribution apparatus 1900 and 1940 serves as a single sensingdevice for both lighting and HVAC functions that are operable on asingle platform by building automation systems (BAS). It is contemplatedthat the BAS may be controllable by a single software system or networkaccessible locally on site or remotely off site. Air distributionapparatus 1900 and 1940 can operate as a single zone or coupled withmultiple like apparatuses for multi-zone operation. Air distributionapparatus 1900 and 1940 is a high turndown, self-balancing system whichallows for continuous commissioning with built-in fault diagnosticsystems. It may be used as a supply, return, or exhaust, or acombination thereof.

One improvement of air distribution apparatus 1900 and 1940 possess isin the difference in method of reporting CFM's. Very low airflows may bemeasured in any LFFC by reducing the opening area to raise the airflowthrough the opening to about 600 FPM, assuming a transducer has at leasta 0.02″ measurement sensitivity. In air distribution apparatus 1900 and1940, airflow discharges directly into occupied space, at velocitiesoften far less than 600 FPM, so CFM's must be determined by other means.A ducted LFFC is generally employed upstream of a group of apparatus1900/1940 to maintain for example 0.08″ in the ductwork supplying thegroup. After initial one-time-only auto-calibration to obtain and storeflow coefficients for the installed connecting ductwork and flexconnections to the downstream devices 1900 and 1940, the upstream LFFCcontroller is able to determine CFM's for all downstream devices evenwhere their discharge velocities are well below 600 FPM.

By means similar to that described elsewhere herein, the air handlingunit together with the upstream LFFC's provide just enough air to keepall air distribution apparatus 1900 and 1940 satisfied and at least onewide open, thereby minimizing at every moment total energy consumptionas well as flow-generated noise.

As outlined above, after the one-time auto-calibration to determine andstore ductwork resistances, the upstream IDD can calculate the CFM ofall the downstream air distribution apparatus 1900 and 1940 given theirrespective % open and the total flow at the upstream IDD. Apparatus 1900and 1940 CFM's may become important when outside temperature is higherthan the approximate 87-89 F return temperature, so that AHU is in MOAmode and minimum ventilation CFM must be maintained; ˜3 if unoccupied,plus 7.5× number of occupants, usually 0 or 1, occasionally 2 in the100-120 ft² zones. The central controller reports % OA to the IDD's inthis mode so the CFM delivered at each apparatus 1940/1944 is able atall times to meet the minimum ventilation requirement based on zoneoccupancy.

Referring now to FIGS. 19E and 19F, another embodiment of airdistribution apparatus 1940 is generally shown. In this embodiment, arotary actuator 1942 controls the position of side troffer plate 1944which is articulable between a closed position and an open positionaround pivot 1946. Side troffer plate 1944 is fixedly attached to a gearsegment 1948 that comprises an arcuate slot ‘950 and a plurality ofteeth 1952. Teeth 1952 of gear segment 1948 engage pinion gear 1954whose rotation articulates gear segment 1948 along an arc within therange of slot 1950. When side troffer plate 1944 is in the openposition, an air flow passage F is defined between side troffer plate1944 and a bottom flange 1956 and is in fluid communication with plenum1909. Those skilled in the art can will realize that side troffer plate1944 and housing bottom flange 1956 extends approximately the entirelength of air distribution apparatus 1940, and hence, when in the openposition, forms a channel for air flow passage F. A gasket 1964 embeddedin a slot in the housing 1956 seals airflow passage F when side trofferplate 1944 is in a closed position.

Referring to FIGS. 19G and 19H, an alternative to the rotary actuator1942 is shown in FIGS. 19E and 19F. A linear actuator or rotary actuatorcontinuous with a threaded shaft 1970 may be implemented to articulatethe position of side troffer plates 1944. In such actuator embodiments,a threaded shaft 1970 is linearly or rotatably driven by an actuatormotor 1972 and wherein an attached or threaded link 1974 engages shaft1970 such that extension or rotation of shaft 1970 moves link 1974linearly along the Y-axis. Link 1974 is hingeably connected to arms1976, 1978, 1980. Combination arms 1976 and 1978 may be used, as shownin FIG. 19G or a single arm 1908 may be used, as shown in FIG. 19H. Anarm 1978 and 1980 is fixedly attached to the end of the shaft rotatingside troffer plate 1944, and the articulation of link 1974 along theY-axis generates a corresponding articulation of side troffer plate 1944between a closed position and an open position. A shield or cover (notshown) may be used to protect the actuation assemblies from theenvironment and damage, particularly from entanglement with surroundinginsulation.

Air distribution apparatus 1940 further comprises a light source, suchas a plurality of LEDs (light emitting diodes) 1958, tipped back toreduce direct radiation from the small high intensity LEDs so mostemission L_(rad) is directed toward the lower edge of inner trofferplate 1962 where a diffuse highly reflective surface is disposed. Thetransmitted light L_(rad) is reflected from diffuse reflective surface1962 and scattered multi-directionally L_(ref). LEDs 1958 may be used asa light source that can be used for room lighting as well as LiFi signaltransmission. As an alternative to the directly reflected light L_(ref),holes sealed with transparent material (not shown) may be positioned atthe ends of air distribution apparatus 1900 and 1940 such that LiFisignal transmission can propagate out in various directions in theabove-ceiling space to provide signal coverage not only within theilluminated space below the air distribution apparatus 1900 and 1940,but in the above-ceiling space as well where required, as over walls.Small auxiliary LiFi sources and sensors may be disposed in theabove-ceiling portion of the apparatus to enable communication wherethere are barriers in the below-ceiling space. The auxiliary LEDs 1958are tipped back largely out of line of sight, so individually coloredLEDs 1958 may be employed. 97-98% diffuse white reflectors of reflectivesurface 1962 largely merge the LED emissions to produce uniform whiteillumination. RGB (red/green/blue) or RYGB (red/yellow/green/blue) LED'smay be employed, and occupants may control color temperature in theirzone. When four LED high RGB LED strips are used, good initial colorbalance is achieved with current LED's using one blue, six yellow-greenand 13 red LED's in each 4″×5″ block. In a 48″ long air distributionapparatus 1940, nine such blocks might be used on each side of heat sink1932. Some studies have shown that color balance more natural than theblue and yellow phosphor balance of current LED and fluorescentluminaires improves worker satisfaction and productivity, so it is notonly a matter of aesthetics. Using three or four LED colors willultimately provide the most efficient as well as satisfying source ofillumination. It is feasible to incorporate R, G, (Y) and B LEDs into asingle envelope, and this eliminates the difficulty of achieving uniformwhite illumination that occurs using discrete R, G, (Y) and B LEDs, andit is contemplated this is form of LED could be incorporated. A largenumbers of LEDs need not be driven hard to produce desired illumination,and this along with heat sink 1832 and incorporated forced convectionheat exchanger yield very long LED lifetimes, such as for example,100,000 hours or more. It is estimated that a 2′×4′ air distributionapparatus 1940 can provide illumination and conditioning to about100-120 ft² of space and a 2′×2′ air distribution apparatus 1940 toabout 64-100 ft² of space.

Energy savings is realized by conducting the heat generated by the LEDbank 1958 to the ceiling plenum above. Unlike fluorescent sources,visible light LED's do not radiate heat and all heat losses areconductive. According to a recent U.S. Department of Energy BetterBuildings report, lighting currently accounts for 34% of energyconsumption in small offices and 40% in large offices. Coupled with thefact that the 82% of LED power consumption not emitted as light iscarried away by conductive heat transfer, this results in a means ofreducing MER fan power consumption by a factor of about three. In atypical office scenario with LED light troffers in which workspace heatload raises 55° F. supply air to 78° F. at the ceiling, LED conductiveheat loss accounts for 0.82×34% (40%)=28% (resp. 33%) of the totalenergy consumption. Removing the heat load from the workspaceimmediately reduces the CFM required to maintain 78° F. at the ceilingby the same factor. Air distribution apparatus 1800 achieves this bydirecting return air over a convective heat exchanger carrying the LEDgenerated heat into the ceiling return plenum, from which it is drawninto a return shaft. All else being equal, MER fan power is reduced to0.72³=0.37, resp. 0.67³=0.3, of the value obtained in the absence of airdistribution apparatus 1800. The temperature in the ceiling returnplenum and shaft is correspondingly raised toT _(ret)=55° F.+23° F./0.72(resp. 0.67)=87° F. (resp. 89° F.),

so they should be well insulated; in particular, high R ceiling tilesshould be employed. The higher return temperature and correspondinglylower CFM facilitate raising efficiency on the chilled water side of thesystem as well.

Air distribution apparatus 1900 and 1940 also controls air supply to theregion it supplies with light, which is typically around 100 squarefeet, or, if alternated with return-only troffers, to about twice thatarea, or 200 square feet. Side troffer plate 1812 on each side of airdistribution apparatus 1800 controls bidirectional horizontal airflowfrom air distribution apparatus 1800. Using sensors TP 1834 upstream andsensor SP 1836 downstream of side troffer plates 1812, the controlcharacteristic is modeled by

${{Flow} = {{C\mspace{11mu} A_{0}\sqrt{2\;\Delta\;{p/}}\rho\mspace{14mu}{with}\mspace{14mu} C} \cong \frac{.61}{1 - {{.39}\mspace{14mu}\left( {\%\mspace{14mu}{open}} \right)^{2}}}}},$

the correlation described elsewhere herein. The present device is ineffect an LFFC embedded in a light troffer which may incorporate many orall sensory and communications described herein.

The flow coefficient curve C enables accurate flow measurement down to afew percent of full flow and control down to virtually zero flow,limited only by any inadvertent leakage out of air distributionapparatus 1900 and 1940. The actual factory calibration curves C arebuilt into the controller. Calibrated accuracy is virtually independentof supply air inhomogeneities and other external factors; therefore, noon site commissioning is required.

Temperature sensors and controller on each air distribution apparatus1900 and 1940 adjust side troffer plates 1912 to maintain temperature asset (standard) in wireless communication with a control room, fancontroller, and a mobile phone or computer application (via WiFi/LiFi)programmed individually to allow individual adjustability of airdistribution apparatus 1900 immediately above each occupant's workspace.Intensity and color temperature control for each air distributionapparatus 1900 and 1940 is available and such controls are alsoavailable in the control room and also to supervisors.

Infrared or visual monitors, such as cameras, may be incorporated intothe overall control scheme of each air distribution apparatus 1900 and1940 to detect occupancy. Such occupancy sensors on each airdistribution apparatus 1900 and 1940 may be set to dim lights and reduceairflow locally in communication with adjacent units in accordance withcurrent occupancy levels. While CO₂ sensors/monitors could be used forthis purpose, their relatively slow response time and low sensitivityand accuracy make separate occupancy sensing preferable. Off-hoursetbacks help conserve energy by turning lights off and further reducingairflow. Small temperature sensors as well as cameras or other sensorsfor occupancy detection may be placed on an insulating layer at thebottom of the LED mounting wedge 1958. Additionally, facial recognitionsoftware may be incorporated with the cameras such that movement fromzone to zone is monitored and user applications, such as WiFi, LiFi,computers lighting, are activated. Facial recognition capability wouldalso allow identification and tracking of specific individuals from zoneto zone as well as flagging of trespassers. This occupancy detectioncapability integral to air distribution apparatus 1900 and 1940 offerssecurity features not otherwise available. Air distribution apparatus1900 and 1940 also comprises fire detection capability wherein smokesensors (not shown) is integrated into the building automation system.Thermal sensors may also be implemented to achieve the aforementionedfunctions. The following is an example of a model of a central-localcontrol implementation for air distribution apparatus 1900 and 1940.Parameters used by an air distribution apparatus 1900 and 1940 andcentral controllers are as follows:

T_(z)=zone temperature, measured by AirLume controller

T_(t)=Target temperature used by AirLume controller

T_(u)=user temperature setting

T_(s)=supply air temperature at AirLume controller

T_(c)=centrally set setback temperature

T_(o)=outside air temperature used by central controller

Operation. MER supplies 55° F. air. In each zone, user sets T_(u) asdesired. T_(t)=T_(u) in occupied zones, reverts to centrally set T_(c)when space remains unoccupied for 10 minutes, for example, andimmediately back to T_(u) when occupancy resumes.

Outline of Normal Mode: Airlume displays Flag1 to central controllerwhile side troffer plates 1812 are wide open and T_(z)>T_(t)−0.5 F; andFlag 2 if wide open and T_(z)>T_(t)+0.5 F. Central controller polls eachAirlume incrementing fan RPM every 2 minutes, for example, proportionalto the number of Flag 2's observed; decrementing slowly while no flagsare showing. (Therefore, holds steady while some flag 1's and no flag2's are showing). Increment proportionality set for reasonablerelaxation time without significant overshoot. Control zones arerelatively small (100 to 200 square feet), so response times can befairly quick without significant overshoot.

When chillers are operating (To>55 F) central controller sets MOAaccording to occupancy, obtained by polling all Airlumes, and return airCO₂ monitors; either at each floor's return opening or with a singlecentral return air MER monitor.

While T_(z)<T_(t)−0.5 F at a perimeter, controller goes into MOA mode,controlling CFM using whatever occupancy sensors are employed andactivating perimeter heat at that location. See Perimeter Heating andMixed Mode below.

Setback modes (unoccupied zones)

During Business Hours, if To≥82° F.+0.5° F., maintain Tz<˜82 F. IfTo≤65° F.−0.05 F at a perimeter Airlume, activate perimeter heat (seebelow) to maintain Tz>˜65° F.

Off Hours: If To≥90 F, maintain Tz<˜Ts=90° F. (Chillers cycle on). IfTo≤50° F., maintain Tz>˜Ts=50° F. (Large MER unit heater or CW/HW coilset to H mode cycles on).

Weekend: If To≥95° F., maintain Tz<˜Ts=95° F. (Chillers cycle on). IfTo≤32° F., maintain Tz>˜T s=32° F. (Large MER unit heater or HW/CW coilset to H) cycles on).

Morning Startup, Winter. Using large MER unit heater or central HW/CWcoils set to H mode, MER supplies 90° F. air to air distributionapparatus 1800, with side troffer plates 1812 initially set wide open orto individual presets designed to balance startup airflow, and FLAG 2set. Perimeter heat may be engaged as well. While T_(z)>T_(t)−0.5° F.air distribution apparatus 1800 controller closes damper and resets Flag2. Sets FLAG 1 while T_(z)>T_(t)+0.5° F. T_(t)=T_(c) except in areasoccupied by maintenance workers.

Normal operation resumes when the number of FLAG 1's exceeds the numberof FLAG 2's.

Morning Startup, Summer. Normal operation except side troffer plates1812 are initialized wide open or to preset values to balance startupairflow.

Perimeter Heating. The 87° F. to 89° F. ceiling plenum temperature isideal for winter heating of office windows, particularly on the floorabove. Very low pressure fans feed grills at the base of windows on thefloor above, and controlled by proximate Airlumes located above. If thebasement is not conditioned, a higher velocity downwash unit is placedin the first floor ceiling plenum.

Mixed Mode. When there are many calls for both heating and cooling, TheCentral System can alternate brief periods of 55 F and 90 F supply air.Central control orchestrates shutting off the open Airlumes and openingthe closed ones when switching back and forth between 55 F and 90 Fsupply air. Mode ends when no Airlumes remain in H mode.

As with all systems designed around LFFC devices, no expensive anduneconomical VAV/reheat boxes are employed in Airlume-based systems.

A standard 24 foot×48 foot air distribution apparatus extendsapproximately 9 inches into the ceiling plenum. An intake on the side orend facilitates running supply ducts low in the ceiling plenum, betweenthe rows of like air distribution apparatuses 1800, to both reduce heattransfer between the supply ducts and warm return plenum and leave aclear return path to the return shaft.

Although the subject matter has been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the subject matter defined in the appended claims is notnecessarily limited to the specific features or acts described above.Rather, the specific features and acts described above are disclosed asexample forms of implementing the claims. In particular the indicatedtemperature and timing values as well as signaling protocols are to betaken as examples.

What is claimed is:
 1. A fluid flow control apparatus adapted for fluidflow therethrough in a flow region extending along a flow axis andlaterally bounded by a tubular inward facing surface of a supportstructure from an upstream end to a downstream end of the flow region,comprising: A. a low flow blade set, and a high flow blade set disposedin the support structure, wherein the low flow blade set includes atleast one blade and the high flow blade set includes at least one blade, wherein edges of the respective blades and the inward facing surfacedefine an array of one or more adjustable cross-section area variableapertures characterized by area A_(o) within the bounds of the inwardfacing surface and define fluid flow paths therethrough between anupstream portion of the flow region between the blades and the upstreamend and a downstream portion of the fluid region between the blades andthe downstream end, wherein A_(o) is representative an aggregate ofareas of cross-sections of the apertures of the array of aperturesnormal to fluid flow paths passing through the apertures, and  whereinthe blades of the low flow blade set and the high flow blade set areeach pivotable about an associated one of a set of mutually parallelpivot axes, between: i. closed angular orientations where edges ofadjacent blades overlap and are adjacent, and edges of blades which arenot adjacent to other blades are adjacent to the inward facing surface,with no portion of the fluid flow path extending past (a) theoverlapping edges of the blades of the blade sets and (b)non-overlapping edges of blades which are adjacent to the inward facingsurface; and ii. open angular orientations angularly offset from theclosed orientations thereby establishing a portion of the fluid flowpath extending past the blades of the blade sets; B. an actuatorassembly including at least one actuator; C. a linkage assembly havingat least one end effector coupling the blades of the respective bladesets to the at least one actuator of the actuator assembly; and D. acontroller responsive to: i. an upstream pressure upstream of the lowflow blade set and the high flow blade set and a downstream pressuredownstream of the low flow blade set and the high flow blade set, togenerate a pressure difference signal representative of a differentialpressure ΔP along the flow axis across the low flow blade set and thehigh flow blade set, ii. the actuator assembly to generate an aperturesignal representative of the area A_(o) of the respective aperturesnormal to flow paths of fluid flowing therethrough, iii. the pressuredifference signal, and the aperture signal to generate a damper areacontrol signal, and apply the damper area control signal to the actuatorassembly, in a closed loop manner, wherein the actuator assembly isadapted by way of the at least one end effector to independently controlthe angular orientations of at least one of the blades of each of therespective blade sets whereby fluid flows from the upstream portion ofthe flow region, through the array of apertures and to the downstreamportion of the flow region, wherein the fluid flowing between the arrayof apertures and the downstream portion, is characterized by acorresponding array of vena contractae having an aggregate cross sectionarea A_(c) normal to the fluid flow therethrough, where A_(c) <A_(o) ,and A_(c) is less than the aggregate cross section area normal to fluidflow elsewhere between the array of apertures and the downstreamportion, thereby establishing a contraction coefficient C for aggregatefluid flow along the fluid flow path past the blades of the respectiveblade sets through the array of apertures wherein C =A_(c)/A_(o) whereA_(c) is representative an aggregate of cross section areas of the venacontractae of fluid flowing through the respective apertures of thearray of apertures, and whereby the controller is responsive tocontraction coefficient C, the aperture signal and the pressure signal,to regulate the variable apertures over time in a closed loop manner sothat a set point is attained.
 2. The fluid flow control apparatus ofclaim 1, wherein: A. the linkage assembly includes: i. a linear cam raceassembly including a cam race plate defining a first cam race and asecond cam race disposed thereon; ii. a first linkage including a firstcam follower disposed in the first cam race, wherein the first linkageis operatively connected between the end effector and the low flow bladeset and adapted for activation by the first cam follower in the firstcam race wherein the first cam race controls pivotal motion of the lowflow blade set during the linear motion of the end effector along anactuator axis; iii. a second linkage including a second cam followerdisposed in the second cam race, wherein the second linkage isoperatively connected between the end effector and the high flow bladeset and adapted for activation by the second cam follower in the secondcam race wherein the second cam race controls pivotal motion of the highflow blade set during the linear motion of the end effector along anactuator axis; and B. the actuator assembly includes: an actuatorcoupled to the linkage and having an end effector adapted to selectivelyeffect linear motion of the end effector along an actuator axis.
 3. Thefluid flow control apparatus of claim 2, wherein at least one of theblades of the low flow blade set is operative to open progressivelythrough an initial 30% of the activation from closed, and at least oneof the blades of the high flow blade set is operative to openprogressively from 15% of the activation from closed.
 4. The fluid flowcontrol apparatus of claim 2, further comprising: a stepper motor; athreaded rod rotatably driven by the stepper motor; wherein rotation ofthe threaded rod translates the end effector along the actuator axis. 5.The fluid flow control apparatus of claim 2, further comprising apotentiometer in operative communication with the blades of the low flowblade set and the blades of the high flow blade set wherein thepotentiometer provides feedback on the angular orientations of one orboth the blades of the low flow blade set and the blades of the highflow blade set to the controller.
 6. The fluid flow control apparatus ofclaim 5, wherein the controller comprises a processor and a memorycommunicatively coupled with and readable by the processor and havingstored therein processor-readable instructions that, when executed bythe processor, cause the processor to determine at least one of thefollowing: 1) a pressure differential sensed along the fluid flow pathand across the blades of the low flow blade set, and the blades of thehigh flow blade set; 2) a variable opening area traversing the fluidflow path based on the angular orientations of the of the blades of thelow flow blade set and the blades of the high flow blade set; 3) a flowcoefficient C_(F) based on the variable opening area of the blades ofthe low flow blade set and the blades of the high flow blade set; and 4)a flow rate based on the pressure differential and the flow coefficient.7. The fluid flow control apparatus of claim 5, wherein the flowcoefficient C_(F) is based on a function of a ratio of the variableopening area to a flow path area, and wherein the flow coefficient C_(F)satisfies 0 ≤C_(F)≤1.
 8. The fluid flow control apparatus of claim 2,further comprising a third blade set that includes at least one blade.9. The fluid flow control apparatus of claim 1, wherein: A. the linkageassembly includes: i. a rotatable cam race gear including a first camrace and a second cam race; ii. a first linkage operatively connected tothe low flow blade set and an associated first cam follower disposed inthe first cam race whereby, in response to rotation of the race camgear, the first cam race controls the angular orientation the blades ofthe low flow blade set during rotation of the cam race gear; iii. asecond linkage operatively connected to the high flow blade set and anassociated second cam follower disposed in the second cam race whereby,in response to rotation of the race cam gear, the second cam racecontrols the angular orientation the blades of the high flow blade setduring rotation of the cam race gear; B. an actuator and associatedpinion gear adapted to rotate the cam race gear in response toactivation of the actuator; whereby, in response to activation of theactuator when the blades of the low flow blade set and the blades of thehigh flow blade set are initially both in the closed angularorientations, the blades of the low flow blade set open progressivelyprior to the blades of the high flow blade set.
 10. The fluid flowcontrol apparatus of claim 9, wherein the low flow blade set opensprogressively through an initial 30% of the activation from closed, andthe high flow blade set opens progressively from 15% of the activationfrom closed.
 11. The fluid flow control apparatus of claim 9, whereinthe pivot axes are co-axial, and the first linkage comprises acylindrical shaft disposed about a first of the pivot axes and having anouter radius R₁ , and the second linkage comprises a cylindrical shellshaft disposed about a second of the pivot axes and having an innerradius R₂, where R₁<R₂ , and the cylindrical shaft of the first linkageis rotatably disposed within the cylindrical shell shaft of the secondlinkage.
 12. The fluid flow control apparatus of claim 9, furthercomprising at least one potentiometer in operative communication withthe blades of the low flow blade set and the blades of the high flowblade set wherein the potentiometer provides feedback on the angularorientations of one or both the blades of the low flow blade set and theblades of the high flow blade set to the controller.
 13. The fluidcontrol apparatus of claim 12, wherein the controller comprises aprocessor and a memory communicatively coupled with and readable by theprocessor and having stored therein processor-readable instructionsthat, when executed by the processor, cause the processor to determineat least one of the following: 1) a pressure differential sensed alongthe fluid flow path and across the blades of the low flow blade set, andthe blades of the high flow blade set; 2) a variable opening areatraversing the fluid flow path based on the angular orientations of theof the blades of the low flow blade set and the blades of the high flowblade set; 3) a flow coefficient C_(F) based on the variable openingarea of the blades of the low flow blade set and the blades of the highflow blade set; and 4) a flow rate based on the pressure differentialand the flow coefficient.
 14. The fluid flow control apparatus of claim13, wherein the flow coefficient C_(F) is based on a function of a ratioof the variable opening area to a flow path area, and wherein the flowcoefficient C_(F) satisfies 0 ≤C_(F)≤1.
 15. The fluid flow controlapparatus of claim 9, further comprising at least one potentiometer thatdetermines the angular orientation of the at least one blade in the lowflow blade set or the at least one blade in the high flow blade set. 16.The fluid flow control apparatus of claim 9, further comprising a thirdblade set that includes at least one blade.